You can use what the tree control itself uses. Here's an excerpt from the cm_HintShow message handler for single-line nodes when hmTooltip mode is in effect.
NodeRect := GetDisplayRect(HitInfo.HitNode, HitInfo.HitColumn, True, True, True);
BottomRightCellContentMargin := DoGetCellContentMargin(HitInfo.HitNode, HitInfo.HitColumn
, ccmtBottomRightOnly);
ShowOwnHint := (HitInfo.HitColumn > InvalidColumn) and PtInRect(NodeRect, CursorPos) and
(CursorPos.X <= ColRight) and (CursorPos.X >= ColLeft) and
(
// Show hint also if the node text is partially out of the client area.
// "ColRight - 1", since the right column border is not part of this cell.
( (NodeRect.Right + BottomRightCellContentMargin.X) > Min(ColRight - 1, ClientWidth) ) or
(NodeRect.Left < Max(ColLeft, 0)) or
( (NodeRect.Bottom + BottomRightCellContentMargin.Y) > ClientHeight ) or
(NodeRect.Top < 0)
);
If ShowOwnHint is true, then you should return the node's text as the hint text. Otherwise, leave the hint text blank.
The main obstacle with using that code is that DoGetCellContentMargin is protected, so you can't call it directly. You can either edit the source to make it public, or you can duplicate its functionality in your own function; if you aren't handling the OnBeforeCellPaint event, then it always returns (0, 0) anyway.
The HitInfo data comes from calling GetHitTestInfoAt.