procedure TMyForm.VSTFreeNode(Sender: TBaseVirtualTree; Node: PVirtualNode);
var
  NewFocus: PVirtualNode;
begin
  NewFocus := VST.GetNext(Node);
  if not Assigned(newFocus) then
    NewFocus := VST.GetPrevious(Node);
  if Assigned(NewFocus) then
  begin
    VST.FocusedNode := NewFocus;
    VST.Selected[NewFocus] := True
  end;
end;

procedure TMyForm.VSTFocusChanged(Sender: TBaseVirtualTree; Node: PVirtualNode; Column: TColumnIndex);
begin
  btn1.Enabled := Assigned(Node);
end;

procedure TMyForm.VSTStructureChange(Sender: TBaseVirtualTree; Node: PVirtualNode;
  Reason: TChangeReason);
begin
  { ActionDeleteNode is assigned to the button's Action property; SelectedCount
    is a bit paranoic here because if you use the toAlwaysSelectNode option, at
    least one node should be always selected, so RootNodeCount > 0 could do the
    same here }
  ActionDeleteNode.Enabled := Sender.SelectedCount > 0;
end;

VST.DeleteNode(VST.FocusedNode);
ButtonDeleteNode.Enabled := VST.SelectedCount > 0;