diff --git a/static/style.css b/static/style.css
index b031db52..d4620e57 100644
--- a/static/style.css
+++ b/static/style.css
@@ -3247,6 +3247,14 @@
 .ws-dropdown-footer{left:0;right:auto;bottom:calc(100% + 4px);min-width:280px;max-width:min(420px,calc(100vw - 32px));}
 .model-dropdown{display:none;position:absolute;bottom:calc(100% + 4px);left:0;min-width:280px;max-width:min(420px,calc(100vw - 32px));background:var(--surface);border:1px solid var(--border2);border-radius:10px;box-shadow:0 -4px 24px rgba(0,0,0,.4);z-index:200;overflow:hidden;max-height:min(70vh,640px);overflow-y:auto;}
 .model-dropdown.open{display:block;}
+/* Phone path (#6080): the model picker is reparented to <body> and switched to
+   position:fixed by _positionModelDropdown() so it escapes the .composer-footer
+   containing block (container-type:inline-size, plus a backdrop-filter under the
+   Geist Contrast skin — both establish a fixed containing block that would
+   otherwise resolve `fixed` against the FOOTER, dropping the menu below the
+   fold). Same idiom as #profileDropdown. JS owns left/top/width/maxHeight; this
+   rule only flips positioning and relaxes the desktop width clamps. */
+.model-dropdown.model-dropdown--floating{position:fixed;left:0;bottom:auto;min-width:0;}
 .model-scope-note{position:sticky;top:0;z-index:2;padding:9px 14px;border-bottom:1px solid var(--border);color:var(--text);font-size:11px;font-weight:650;line-height:1.4;background:color-mix(in srgb,var(--surface) 82%,var(--accent-bg));box-shadow:0 1px 0 rgba(0,0,0,.12);}
 .model-group{padding:8px 14px 4px;font-size:10px;font-weight:700;letter-spacing:.04em;color:var(--muted);text-transform:uppercase;border-top:1px solid var(--border2);margin-top:2px;}.model-group.collapsible{cursor:pointer;user-select:none}.model-group.collapsible:before{content:'\25b6';display:inline-block;font-size:8px;margin-right:5px;transition:transform .15s ease}.model-group.collapsible.open:before{transform:rotate(90deg)}.model-group-body:empty{display:none}
 .model-group.sub{padding:4px 14px 2px 22px;font-size:9px;border-top:none;margin-top:0;letter-spacing:.03em;color:var(--muted);background:transparent;}.model-group.sub.collapsible:before{content:'\25b6';display:inline-block;font-size:7px;margin-right:4px;transition:transform .15s ease}.model-group.sub.collapsible.open:before{transform:rotate(90deg)}.model-group-body.sub{padding-left:8px;border-left:1px solid var(--border);}
diff --git a/static/ui.js b/static/ui.js
index f4d66e18..a71b9bf7 100644
--- a/static/ui.js
+++ b/static/ui.js
@@ -3714,6 +3714,35 @@ function syncModelChip(){
   if(mobileAction) mobileAction.classList.toggle('active',!!(dd&&dd.classList.contains('open')));
 }
 
+// Remembers where #composerModelDropdown lives in the composer-footer so the
+// phone path can move it to <body> and put it back exactly. Captured lazily on
+// the first reparent (see _positionModelDropdown phone branch).
+let _modelDropdownHome=null;
+
+// Return the model dropdown into its original .composer-footer slot and clear
+// every inline style the phone path wrote, so the desktop CSS (position:absolute
+// anchored on the relatively-positioned .composer-footer) fully governs again.
+// Safe to call when the element never moved — it just no-ops the reinsert.
+function _restoreModelDropdownHome(){
+  const dd=document.getElementById('composerModelDropdown');
+  if(!dd) return;
+  dd.classList.remove('model-dropdown--floating');
+  dd.style.left='';
+  dd.style.top='';
+  dd.style.bottom='';
+  dd.style.width='';
+  dd.style.maxWidth='';
+  dd.style.maxHeight='';
+  if(_modelDropdownHome&&_modelDropdownHome.parent&&dd.parentNode!==_modelDropdownHome.parent){
+    const ref=_modelDropdownHome.nextSibling;
+    if(ref&&ref.parentNode===_modelDropdownHome.parent){
+      _modelDropdownHome.parent.insertBefore(dd,ref);
+    }else{
+      _modelDropdownHome.parent.appendChild(dd);
+    }
+  }
+}
+
 function _positionModelDropdown(){
   const dd=$('composerModelDropdown');
   const chip=$('composerModelChip');
@@ -3723,9 +3752,62 @@ function _positionModelDropdown(){
   const panel=$('composerMobileConfigPanel');
   const anchor=(panel&&panel.classList.contains('open')&&mobileAction)?mobileAction:(chip&&chip.offsetParent?chip:mobileAction);
   if(!anchor) return;
-  const chipRect=anchor.getBoundingClientRect();
+  const isPhone=typeof window.matchMedia==='function'&&window.matchMedia('(max-width:640px)').matches;
+  if(isPhone){
+    // #6080: .composer-footer sets container-type:inline-size (and a
+    // backdrop-filter under the Geist Contrast skin) — both establish a fixed
+    // containing block, so a position:fixed dropdown left inside the footer
+    // resolves against the FOOTER (bottom of screen) instead of the viewport
+    // and lands below the fold. Reparent to <body> — exactly the working
+    // #profileDropdown idiom — so position:fixed is viewport-relative on ALL
+    // skins, then compute coordinates against the visual viewport.
+    if(!_modelDropdownHome){
+      _modelDropdownHome={parent:dd.parentNode,nextSibling:dd.nextSibling};
+    }
+    if(dd.parentNode!==document.body) document.body.appendChild(dd);
+    dd.classList.add('model-dropdown--floating');
+    const anchorRect=anchor.getBoundingClientRect();
+    const visualViewport=window.visualViewport;
+    const viewportWidth=Math.max(1,Number(visualViewport&&visualViewport.width)||window.innerWidth||1);
+    const viewportHeight=Math.max(1,Number(visualViewport&&visualViewport.height)||window.innerHeight||1);
+    const viewportTop=Math.max(0,Number(visualViewport&&visualViewport.offsetTop)||0);
+    const viewportBottom=viewportTop+viewportHeight;
+    const margin=8;
+    const gap=6;
+    const viewportLeft=Math.max(0,Number(visualViewport&&visualViewport.offsetLeft)||0);
+    const viewportRight=viewportLeft+viewportWidth;
+    const titlebar=document.querySelector('.app-titlebar');
+    const titlebarBottom=titlebar&&typeof titlebar.getBoundingClientRect==='function'
+      ? Number(titlebar.getBoundingClientRect().bottom)||0
+      : 0;
+    const contentTop=Math.max(viewportTop+margin,titlebarBottom+margin);
+    const menuWidth=Math.max(1,viewportWidth-margin*2);
+    const left=Math.max(viewportLeft+margin,Math.min(anchorRect.left,viewportRight-menuWidth-margin));
+    dd.style.left=`${left}px`;
+    dd.style.width=`${menuWidth}px`;
+    dd.style.maxWidth=`${menuWidth}px`;
+    dd.style.bottom='auto';
+    const menuHeight=Math.max(dd.scrollHeight,dd.offsetHeight);
+    const aboveSpace=Math.max(0,anchorRect.top-contentTop-gap-margin);
+    const belowSpace=Math.max(0,viewportBottom-anchorRect.bottom-gap-margin);
+    const openAbove=aboveSpace>=Math.min(menuHeight,belowSpace)||aboveSpace>=belowSpace;
+    const availableHeight=Math.max(1,openAbove?aboveSpace:belowSpace);
+    dd.style.maxHeight=`${availableHeight}px`;
+    const visibleHeight=Math.min(menuHeight||availableHeight,availableHeight);
+    const top=openAbove
+      ? anchorRect.top-gap-visibleHeight
+      : anchorRect.bottom+gap;
+    dd.style.top=`${Math.max(contentTop,Math.min(top,viewportBottom-margin-visibleHeight))}px`;
+    return;
+  }
+  // Desktop (>640px): keep the current master behaviour — an absolutely
+  // positioned .composer-footer child. Restore the element into the footer (in
+  // case a prior phone open moved it to <body>) and clear the phone inline
+  // styles so the desktop CSS anchor is byte-for-byte identical to master.
+  _restoreModelDropdownHome();
+  const anchorRect=anchor.getBoundingClientRect();
   const footerRect=footer.getBoundingClientRect();
-  let left=chipRect.left-footerRect.left;
+  let left=anchorRect.left-footerRect.left;
   const maxLeft=Math.max(0, footer.clientWidth-dd.offsetWidth);
   left=Math.max(0, Math.min(left, maxLeft));
   dd.style.left=`${left}px`;
@@ -4532,6 +4614,10 @@ function closeModelDropdown(){
   if(dd) dd.classList.remove('open');
   if(chip) chip.classList.remove('active');
   if(mobileAction) mobileAction.classList.remove('active');
+  // If the phone path reparented the menu onto <body>, put it back in the
+  // footer and clear the fixed-position inline styles so the DOM returns to its
+  // baseline shape and the next desktop open anchors correctly (#6080).
+  if(typeof _restoreModelDropdownHome==='function') _restoreModelDropdownHome();
 }
 
 function closeSettingsModelDropdown(){
@@ -4653,6 +4739,26 @@ window.addEventListener('resize',()=>{
   }
 });
 
+// visualViewport resize/scroll fire on mobile when the on-screen keyboard opens
+// or the URL bar collapses/expands — the phone dropdown is fixed to the visual
+// viewport, so it must be re-measured against the new offsets. Coalesce with rAF
+// so a burst of scroll/resize events triggers at most one reposition per frame.
+let _modelDropdownRepositionScheduled=false;
+function _repositionOpenModelDropdown(){
+  const dd=$('composerModelDropdown');
+  if(!(dd&&dd.classList.contains('open'))||_modelDropdownRepositionScheduled) return;
+  _modelDropdownRepositionScheduled=true;
+  requestAnimationFrame(()=>{
+    _modelDropdownRepositionScheduled=false;
+    const openDd=$('composerModelDropdown');
+    if(openDd&&openDd.classList.contains('open')) _positionModelDropdown();
+  });
+}
+if(window.visualViewport){
+  window.visualViewport.addEventListener('resize',_repositionOpenModelDropdown);
+  window.visualViewport.addEventListener('scroll',_repositionOpenModelDropdown);
+}
+
 // ── Fit-based composer footer collapse ──────────────────────────────────────
 // Stage classes on .composer-footer:
 //   (none) full labels · .cf-icons icon chips · .cf-icons.cf-burger hamburger.
diff --git a/tests/test_issue6080_model_picker_reparent.py b/tests/test_issue6080_model_picker_reparent.py
new file mode 100644
index 00000000..855d21bd
--- /dev/null
+++ b/tests/test_issue6080_model_picker_reparent.py
@@ -0,0 +1,279 @@
+"""Regression guards for #6080 — mobile composer model picker lands off-screen.
+
+Root cause: #composerModelDropdown is a child of .composer-footer, which sets
+`container-type:inline-size` (and, under the Geist Contrast skin, a
+`backdrop-filter`). Both establish a fixed containing block, so a phone
+`position:fixed` dropdown resolves against the FOOTER (pinned to the bottom of
+the screen) instead of the visual viewport, dropping the menu below the fold —
+the "tapping the model picker does nothing / opens off-screen" symptom.
+
+Fix (PR #6105 rework, credit @webtecnica): on the phone path the dropdown is
+reparented to <body> and switched to position:fixed via a `--floating` class,
+exactly the working #profileDropdown idiom, so `fixed` is viewport-relative on
+ALL skins. Desktop (>640px) is unchanged: the menu stays an absolutely
+positioned .composer-footer child.
+
+The node-executed test below is the load-bearing one: it runs the real
+`_positionModelDropdown` / `closeModelDropdown` against a stub DOM and asserts
+DOM parentage, i.e. that the dropdown is NOT a descendant of the footer while
+open on a phone (so no container-type ancestor can trap its fixed positioning),
+and that it is restored into the footer on close and on desktop.
+"""
+import json
+import re
+import subprocess
+import textwrap
+from pathlib import Path
+
+REPO_ROOT = Path(__file__).parent.parent.resolve()
+UI_JS = (REPO_ROOT / "static" / "ui.js").read_text(encoding="utf-8")
+CSS = (REPO_ROOT / "static" / "style.css").read_text(encoding="utf-8")
+
+
+def _function_body(src: str, marker: str) -> str:
+    start = src.index(marker)
+    depth = 0
+    opened = False
+    for idx, ch in enumerate(src[start:], start):
+        if ch == "{":
+            depth += 1
+            opened = True
+        elif ch == "}":
+            depth -= 1
+            if opened and depth == 0:
+                return src[start : idx + 1]
+    raise AssertionError(f"Could not extract function body for {marker}")
+
+
+# ── Static structure guards ──────────────────────────────────────────────────
+
+def test_css_has_floating_fixed_rule():
+    """The reparented phone menu needs a body-level position:fixed rule."""
+    m = re.search(r"\.model-dropdown\.model-dropdown--floating\{([^}]*)\}", CSS)
+    assert m, ".model-dropdown--floating rule missing (phone reparent CSS)"
+    body = m.group(1)
+    assert "position:fixed" in body, (
+        "floating model dropdown must be position:fixed so it anchors to the "
+        "viewport once reparented to <body> (#6080)"
+    )
+
+
+def test_no_geist_backdrop_override_added_for_model_dropdown():
+    """Because the menu leaves the footer, the Geist backdrop-filter workaround
+    must NOT be introduced (the reparent is the fix, not a per-skin override)."""
+    assert "container-type:normal" not in CSS.replace(" ", ""), (
+        "do not neutralise container-type on the footer — reparent instead"
+    )
+
+
+def test_position_fn_has_phone_reparent_branch():
+    body = _function_body(UI_JS, "function _positionModelDropdown(")
+    assert "matchMedia('(max-width:640px)')" in body, "phone breakpoint check missing"
+    assert "document.body.appendChild(dd)" in body, (
+        "phone path must reparent the dropdown to <body> to escape the "
+        ".composer-footer containing block (#6080)"
+    )
+    assert "model-dropdown--floating" in body, "phone path must apply the floating class"
+    # PR #6105 visual-viewport math must be preserved.
+    assert "window.visualViewport" in body
+    assert "titlebar" in body and "app-titlebar" in body, "titlebar clamp preserved"
+    assert "openAbove" in body, "above/below flip preserved"
+    assert "menuWidth" in body and "margin*2" in body, "width=viewport-16px preserved"
+
+
+def test_close_restores_home_parent():
+    body = _function_body(UI_JS, "function closeModelDropdown(")
+    assert "_restoreModelDropdownHome" in body, (
+        "closeModelDropdown must return the reparented menu to the footer"
+    )
+
+
+def test_raf_coalesced_visualviewport_listeners_present():
+    assert "_repositionOpenModelDropdown" in UI_JS
+    assert "requestAnimationFrame" in _function_body(UI_JS, "function _repositionOpenModelDropdown(")
+    assert "window.visualViewport.addEventListener('resize',_repositionOpenModelDropdown)" in UI_JS
+    assert "window.visualViewport.addEventListener('scroll',_repositionOpenModelDropdown)" in UI_JS
+
+
+# ── Load-bearing DOM-parentage guard (executed in node) ──────────────────────
+
+def test_dropdown_escapes_footer_containing_block_when_open_on_phone():
+    """Prove via real execution that the open phone dropdown is reparented to
+    <body> and is NOT a descendant of .composer-footer (the container-type
+    ancestor), and that it is restored into the footer on close / on desktop."""
+    block_start = UI_JS.index("let _modelDropdownHome=null;")
+    block_end = UI_JS.index("function _readModelOverflowData(")
+    position_block = UI_JS[block_start:block_end]
+    close_block = _function_body(UI_JS, "function closeModelDropdown(")
+    snippets = [position_block, close_block]
+
+    script = textwrap.dedent(
+        f"""
+        const assert = require('assert');
+        const snippets = {json.dumps(snippets)};
+
+        class ClassList {{
+          constructor(el) {{ this.el = el; this.set = new Set(); }}
+          add(n) {{ this.set.add(n); this._sync(); }}
+          remove(n) {{ this.set.delete(n); this._sync(); }}
+          contains(n) {{ return this.set.has(n); }}
+          toggle(n, f) {{
+            if (f === undefined) f = !this.set.has(n);
+            if (f) this.add(n); else this.remove(n);
+            return f;
+          }}
+          _sync() {{ this.el.className = [...this.set].join(' '); }}
+        }}
+        class Node {{
+          constructor(tag, id) {{
+            this.tagName = (tag || 'div').toUpperCase();
+            this.id = id || '';
+            this.className = '';
+            this.classList = new ClassList(this);
+            this.style = {{}};
+            this.children = [];
+            this.parentNode = null;
+            this.dataset = {{}};
+            this._rect = {{left:0, top:0, right:0, bottom:0, width:0, height:0}};
+            this.scrollHeight = 0; this.offsetHeight = 0;
+            this.offsetWidth = 0; this.clientWidth = 0;
+            this.offsetParent = null;
+          }}
+          _detach(child) {{
+            const i = this.children.indexOf(child);
+            if (i >= 0) this.children.splice(i, 1);
+            child.parentNode = null;
+          }}
+          appendChild(child) {{
+            if (child.parentNode) child.parentNode._detach(child);
+            child.parentNode = this; this.children.push(child); return child;
+          }}
+          insertBefore(child, ref) {{
+            if (child.parentNode) child.parentNode._detach(child);
+            child.parentNode = this;
+            const i = ref ? this.children.indexOf(ref) : -1;
+            if (i >= 0) this.children.splice(i, 0, child);
+            else this.children.push(child);
+            return child;
+          }}
+          get nextSibling() {{
+            if (!this.parentNode) return null;
+            const i = this.parentNode.children.indexOf(this);
+            return this.parentNode.children[i + 1] || null;
+          }}
+          getBoundingClientRect() {{ return this._rect; }}
+        }}
+
+        const body = new Node('body', 'body');
+        const footer = new Node('div');            // .composer-footer (container-type ancestor)
+        footer.className = 'composer-footer';
+        footer.clientWidth = 390;
+        footer._rect = {{left:0, top:560, right:390, bottom:600, width:390, height:40}};
+        const titlebar = new Node('div');
+        titlebar.className = 'app-titlebar';
+        titlebar._rect = {{left:0, top:0, right:390, bottom:44, width:390, height:44}};
+
+        const dd = new Node('div', 'composerModelDropdown');
+        dd.scrollHeight = 300; dd.offsetHeight = 300; dd.offsetWidth = 280;
+        const chip = new Node('button', 'composerModelChip');
+        chip.offsetParent = footer;   // visible on the desktop composer
+        chip._rect = {{left:100, top:560, right:160, bottom:600, width:60, height:40}};
+        const mobileAction = new Node('button', 'composerMobileModelAction');
+        mobileAction.offsetParent = footer;
+        mobileAction._rect = {{left:20, top:560, right:120, bottom:600, width:100, height:40}};
+        const panel = new Node('div', 'composerMobileConfigPanel');
+
+        // dd starts life inside the footer, followed by a sibling — proves the
+        // insertBefore restore path returns it to the exact original slot.
+        const trailingSibling = new Node('div', 'uploadBarWrap');
+        footer.appendChild(dd);
+        footer.appendChild(trailingSibling);
+
+        const elements = new Map([
+          ['composerModelDropdown', dd],
+          ['composerModelChip', chip],
+          ['composerMobileModelAction', mobileAction],
+          ['composerMobileConfigPanel', panel],
+        ]);
+
+        let PHONE = true;
+        globalThis.document = {{
+          body,
+          getElementById: (id) => elements.get(id) || null,
+          querySelector: (sel) => {{
+            if (sel === '.composer-footer') return footer;
+            if (sel === '.app-titlebar') return titlebar;
+            return null;
+          }},
+        }};
+        globalThis.window = {{
+          matchMedia: (q) => ({{ matches: q.indexOf('max-width:640px') !== -1 ? PHONE : false }}),
+          innerWidth: 390, innerHeight: 800,
+          visualViewport: {{ width: 390, height: 600, offsetTop: 0, offsetLeft: 0 }},
+        }};
+        globalThis.$ = (id) => elements.get(id) || null;
+
+        eval(snippets.join(String.fromCharCode(10)) + String.fromCharCode(10) + `;globalThis.__t = {{
+          position: _positionModelDropdown,
+          close: closeModelDropdown,
+          restore: _restoreModelDropdownHome,
+        }};`);
+
+        function ancestorIsFooter(el) {{
+          let p = el.parentNode;
+          while (p) {{ if (p === footer) return true; p = p.parentNode; }}
+          return false;
+        }}
+
+        // ── Phone: open ──────────────────────────────────────────────────────
+        PHONE = true;
+        dd.classList.add('open');
+        __t.position();
+        assert.strictEqual(dd.parentNode, body,
+          'open phone dropdown must be reparented to <body>');
+        assert.notStrictEqual(dd.parentNode, footer,
+          'open phone dropdown must NOT remain a footer child');
+        assert.strictEqual(ancestorIsFooter(dd), false,
+          'open phone dropdown must have NO .composer-footer ancestor — this is ' +
+          'what escapes the container-type/backdrop-filter fixed-containing-block trap (#6080)');
+        assert.strictEqual(dd.classList.contains('model-dropdown--floating'), true,
+          'phone dropdown must carry the floating (position:fixed) class');
+        assert.ok(dd.style.top && dd.style.top.endsWith('px'), 'phone path sets a px top');
+        assert.ok(dd.style.width && dd.style.width.endsWith('px'), 'phone path sets a px width');
+
+        // ── Phone: close restores it to the exact original footer slot ───────
+        __t.close();
+        assert.strictEqual(dd.parentNode, footer,
+          'closed dropdown must be restored into .composer-footer');
+        assert.strictEqual(dd.nextSibling, trailingSibling,
+          'restore must reinsert the dropdown before its original next sibling');
+        assert.strictEqual(dd.classList.contains('model-dropdown--floating'), false,
+          'close must drop the floating class');
+        assert.strictEqual(dd.style.top, '', 'close must clear the fixed inline top');
+        assert.strictEqual(dd.style.width, '', 'close must clear the inline width');
+
+        // ── Desktop: never reparents, stays an absolutely positioned footer child ──
+        PHONE = false;
+        dd.classList.add('open');
+        __t.position();
+        assert.strictEqual(dd.parentNode, footer,
+          'desktop dropdown must stay inside .composer-footer (behaviour identical to master)');
+        assert.strictEqual(dd.classList.contains('model-dropdown--floating'), false,
+          'desktop dropdown must not use the floating class');
+        assert.ok(dd.style.top === '' || dd.style.top === undefined || dd.style.top === null,
+          'desktop path must not write a fixed top');
+
+        console.log('OK');
+        """
+    )
+    proc = subprocess.run(
+        ["node", "-e", script],
+        cwd=REPO_ROOT,
+        check=False,
+        text=True,
+        capture_output=True,
+    )
+    assert proc.returncode == 0, (
+        f"node DOM-parentage assertions failed:\n{proc.stdout}\n{proc.stderr}"
+    )
+    assert "OK" in proc.stdout