  The (non-spanning) tree-decorated quadrangulation is a random pair formed by
a quadrangulation and a subtree chosen uniformly over the set of pairs with
prescribed size. In this paper we study the tree-decorated quadrangulation in
the critical regime: when the number of faces of the map, $f$, is proportional
to the square of the size of the tree. We show that with high probability in
this regime, the diameter of the tree is between $o(f^{1/4})$ and
$f^{1/4}/\log^\alpha(f)$, for $\alpha >1$. Thus after scaling the distances by
$f^{-1/4}$, the critical tree-decorated quadrangulation converges to a Brownian
disk where the boundary has been identified to a point. These results imply the
triviality of the shocked map: the metric space generated by gluing a Brownian
disk with a continuous random tree.
