Packing and covering immersion-expansions of planar sub-cubic graphs

A graph H is an immersion of a graph G if H can be obtained by some subgraph G after lifting incident edges. We prove that there is a polynomial function f:N×N→N, such that if H is a connected planar sub-cubic graph on h>0 edges, G is a graph, and k is a non-negative integer, then either G contains k vertex/edge-disjoint subgraphs, each containing H as an immersion, or G contains a set F of f(k,h) vertices/edges such that G∖F does not contain H as an immersion.