On the Erdos-Posa property for immersions and topological minors in tournaments

We consider the Erdos-Posa property for immersions and topological minors in tournaments. We prove that for every simple digraph H, k is an element of N, and tournament T, the following statements hold: If in T one cannot find k arc-disjoint immersion copies of H, then there exists a set of O-H(k(3)) arcs that intersects all immersion copies of H in T. If in T one cannot find k vertex-disjoint topological minor copies of H, then there exists a set of O-H(k log k) vertices that intersects all topological minor copies of H in T. This improves the results of Raymond [DMTCS '18], who proved similar statements under the assumption that H is strongly connected.