  For a finite collection of graphs ${\cal F}$, the \textsc{${\cal
F}$-TM-Deletion} problem has as input an $n$-vertex graph $G$ and an integer
$k$ and asks whether there exists a set $S \subseteq V(G)$ with $|S| \leq k$
such that $G \setminus S$ does not contain any of the graphs in ${\cal F}$ as a
topological minor. We prove that for every such ${\cal F}$, \textsc{${\cal
F}$-TM-Deletion} is fixed parameter tractable on planar graphs. Our algorithm
runs in a $2^{\mathcal{O}(k^2)}\cdot n^{2}$ time or, alternatively in
$2^{\mathcal{O}(k)}\cdot n^{4}$ time. Our techniques can easily be extended to
graphs that are embeddable on any fixed surface.
