diff --git a/frontend/packages/dashboard/src/app.js b/frontend/packages/dashboard/src/app.js
index 49394ce..d2d8d93 100644
--- a/frontend/packages/dashboard/src/app.js
+++ b/frontend/packages/dashboard/src/app.js
@@ -649,16 +649,29 @@ window.marked = marked;
     }
     return out;
   }
-  function treePrefix({ depth, ancestorIsLast, isLast }) {
-    if (depth === 0) return '';
-    let s = '';
-    // Ancestor at depth 0 (root) doesn't get a vertical-line column —
-    // roots are separated visually as top-level rows already.
+  // Builds the .tree-prefix DOM for a row at the given depth. Each
+  // lane is its own positioned child so CSS can paint full-height
+  // vertical bars that bridge the gap between sibling rows — text
+  // box-drawing glyphs only paint one text-line tall, which left
+  // visible breaks between rows once we grew taller-than-one-line
+  // container cards (#388). Ancestor lanes are either continuation
+  // (vertical bar top→bottom+gap) or blank; the joint at this row's
+  // own depth is ├ (branch — vertical continues below) or └ (last —
+  // vertical stops at the row's icon midline). CSS at
+  // `.container-row .tree-prefix` paints the bars + horizontal stub.
+  function treePrefixDom({ depth, ancestorIsLast, isLast }) {
+    if (depth === 0) return null;
+    const prefix = el('span', { class: 'tree-prefix', 'aria-hidden': 'true' });
+    // Ancestor columns (depth 1..depth-1). Skip depth 0 (root has no
+    // continuation column — top-level rows are separated visually as
+    // top-level rows already).
     for (let d = 1; d < depth; d++) {
-      s += ancestorIsLast[d] ? '   ' : '│  ';
+      const cls = ancestorIsLast[d] ? 'tree-lane lane-blank' : 'tree-lane lane-line';
+      prefix.append(el('span', { class: cls }));
     }
-    s += isLast ? '└─ ' : '├─ ';
-    return s;
+    const jointCls = 'tree-lane lane-joint ' + (isLast ? 'lane-joint-last' : 'lane-joint-branch');
+    prefix.append(el('span', { class: jointCls }));
+    return prefix;
   }
 
   function renderContainers(s) {
@@ -731,10 +744,8 @@ window.marked = marked;
       // legacy flat layout (every container at depth 0) is bit-
       // identical to today's render — no glyph, no indent.
       if (node.depth > 0) li.dataset.depth = String(node.depth);
-      const prefix = treePrefix(node);
-      if (prefix) {
-        li.prepend(el('span', { class: 'tree-prefix', 'aria-hidden': 'true' }, prefix));
-      }
+      const prefix = treePrefixDom(node);
+      if (prefix) li.prepend(prefix);
 
       // Full-height square agent icon, left of the card body. The
       // icon is an <img> absolutely positioned inside a wrapper div:
diff --git a/frontend/packages/dashboard/src/dashboard.css b/frontend/packages/dashboard/src/dashboard.css
index 2747613..fa44bbb 100644
--- a/frontend/packages/dashboard/src/dashboard.css
+++ b/frontend/packages/dashboard/src/dashboard.css
@@ -204,18 +204,76 @@ a:hover {
 .container-row[data-depth="4"] { margin-left: 7.2em; }
 .container-row[data-depth="5"] { margin-left: 9em; }
 .container-row[data-depth="6"] { margin-left: 10.8em; }
+/* Tree prefix sits in the left margin and paints the connecting
+   ├ / └ / │ lanes as CSS rules rather than text glyphs (#388). Each
+   ancestor depth gets its own `.tree-lane` so we can paint a
+   full-row-height vertical bar that extends through the
+   .containers row gap into the next sibling — text box-drawing
+   glyphs only fill one text line, which left visible breaks
+   between rows once cards grew taller than one line of text (5em
+   square icons + multi-line body). The horizontal stub at the row's
+   own joint lands at the icon midline so the L/T meets the icon
+   edge cleanly. */
 .container-row .tree-prefix {
-  /* Tree-line glyphs sit in the left margin so the rest of the
-     container card layout (icon + body flex split) stays unchanged.
-     Mono font for column alignment with the ├─ / └─ / │  bricks. */
   position: absolute;
-  left: -1.6em;
-  top: 0.6em;
-  color: var(--purple-dim);
-  font-family: inherit;
-  white-space: pre;
+  /* Extend into the `.containers { gap: 0.4em }` below so vertical
+     bars connect to the next sibling's prefix without a visual gap. */
+  top: 0;
+  bottom: -0.4em;
+  display: flex;
+  flex-direction: row;
   pointer-events: none;
   user-select: none;
+  color: var(--purple-dim);
+}
+/* Each depth step is one 1.8em lane wide — same step as the row's
+   own margin-left ladder above, so the rightmost lane (the joint)
+   sits flush against the row content (the icon). The prefix's left
+   edge is depth*1.8em LEFT of the row's left edge, so its right
+   edge meets the icon, and the leftmost lane lines up with the
+   top-level rows' icons at x=0. */
+.container-row[data-depth="1"] .tree-prefix { left: -1.8em; }
+.container-row[data-depth="2"] .tree-prefix { left: -3.6em; }
+.container-row[data-depth="3"] .tree-prefix { left: -5.4em; }
+.container-row[data-depth="4"] .tree-prefix { left: -7.2em; }
+.container-row[data-depth="5"] .tree-prefix { left: -9em; }
+.container-row[data-depth="6"] .tree-prefix { left: -10.8em; }
+.tree-prefix .tree-lane {
+  flex: 0 0 1.8em;
+  position: relative;
+}
+/* Continuation bar — full row + gap below (so two adjacent
+   ancestor-line lanes from sibling rows visually merge into one
+   unbroken vertical line). Drawn at lane center (0.6em from left)
+   to keep it visually centered in the 1.8em column. */
+.tree-prefix .lane-line::before,
+.tree-prefix .lane-joint::before {
+  content: '';
+  position: absolute;
+  left: 0.6em;
+  top: 0;
+  bottom: 0;
+  border-left: 1px solid currentColor;
+}
+/* Last-child joint (└): vertical bar stops at the icon midline (no
+   continuation below this row). 3.1em ≈ row padding-top 0.6em +
+   icon half-height 2.5em, matching the horizontal stub's y below. */
+.tree-prefix .lane-joint-last::before {
+  bottom: auto;
+  height: 3.1em;
+}
+/* Horizontal stub from the joint's vertical bar across the lane
+   and through the row's padding-left to the icon left edge. Lands
+   at the icon midline so the ├/└ meets the icon cleanly.
+   Width = lane-right (1.2em from lane center) + row padding-left
+   (0.8em) = 2em. */
+.tree-prefix .lane-joint::after {
+  content: '';
+  position: absolute;
+  left: 0.6em;
+  top: 3.1em;
+  width: 2em;
+  border-top: 1px solid currentColor;
 }
 /* Live cards get the icon-left / body-right split; tombstone rows keep
    the plain stacked block layout. The icon is a background-image div