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For a finite collection of graphs F, the F-TM-Deletion problem has as input an n-vertex graph G and an integer k and asks whether there exists a set S ⊆ V(G) with |S| ≤ k such that G ∖ S does not contain any of the graphs in F as a topological minor. We prove that for every such F, F-TM-Deletion is fixed parameter tractable on planar graphs. Our algorithm runs in a 2^𝒪(k^2)· n^2 time or, alternatively in 2^𝒪(k)· n^4 time. Our techniques can easily be extended to graphs that are embeddable on any fixed surface.arXiv:1907.02919v4 fatcat:mh5f3arvurapjjd7hm5ynkw7cq