The far-apart planar Erdős–Pósa conjecture

Let $H$ be a planar graph. An $H$ minor-model is a model of $H$ in $G$, and minor-models are pairwise distance at least $d$ when every two distinct models are at that distance or farther. Then there is a function $f:\mathbb{N}\to\mathbb{N}$ and a constant $c$ such that for every graph $G$, if $G$ does not contain $n$ disjoint $H$ minor-models that have pairwise distance at least $d$ from each other, then there is a set $Z$ of at most $f(n)$ vertices of $G$ such that $G-B_G(Z,cd)$ contains no $H$ minor. Far-apart planar Erdős–Pósa conjecture.

This conjecturally strengthens the known far-apart-cycle result to arbitrary planar minor-models. The paper presents it after contrasting it with the failure of the general coarse Erdős–Pósa property.