The planar induced-minor Erdős–Pósa conjecture

For a graph $H$, $kH$ denotes the disjoint union of $k$ copies of $H$, and a graph is $H$-induced-minor-free if it does not contain $H$ as an induced minor. The planar induced-minor Erdős–Pósa conjecture. For each planar graph $H$, there exist a function $f$ and a constant $d$ such that, for every positive integer $k$ and every graph $G$, either $G$ contains $kH$ as an induced minor, or there is a set $X$ of at most $f(k)$ vertices such that $G-B_G(X,d)$ is $H$-induced-minor-free. This is an induced-minor analogue of the planar graph-minor Erdős–Pósa theorem. The source gives a bounded-maximum-degree version using an induced grid-minor theorem, but does not resolve the unrestricted conjecture.