Tight bound for the Erdos-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.