Tight bound for the Erd{o}s-P\'osa property of tree minors

Let T be a tree on t vertices. We prove that for every positive integer k and every graph G, either G contains k pairwise vertex-disjoint subgraphs each having a T minor, or there exists a set X of at most $t(k-1)$ vertices of G such that $G-X$ has no T minor. The bound on the size of X is best possible and improves on an earlier $f(t)k$ bound proved by Fiorini, Joret, and Wood (2013) with some very fast growing function $f(t)$. Moreover, our proof is very short and simple.