We consider the Erdős-Pósa property for immersions and topological minors in tournaments. We prove that for every simple digraph $H$, $k\in \mathbb{N}$, and tournament $T$, the following statements hold:
(i) If in $T$ one cannot find $k$ arc-disjoint immersion copies of $H$, then there exists a set of $\mathcal{O}_H(k^3)$ arcs that intersects all immersion copies of $H$ in $T$.
(ii) If in $T$ one cannot find $k$ vertex-disjoint topological minor copies of $H$, then there exists a set of $\mathcal{O}_H(k\log k)$ 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.

Comment: 15 pages, 1 figure

• 05C20 - Directed graphs (digraphs), tournaments
• 05C70 - Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
• 05C83 - Graph minors