Disconnected diagonal pairs in maximal planar graphs

Completely determine all disconnected planar graphs H such that every sufficiently large maximal planar graph, under every red/blue edge-colouring, contains a red copy of H or a blue copy of H.

Background

The paper completely determines the connected graphs H for which the diagonal pair {H, H} is unavoidable in maximal planar graphs: the possibilities are trees on at most four vertices, P_5, and the fork graph S_{2,1,1}. The disconnected case remains unresolved.

The paper establishes several avoidability constructions for disconnected graphs, but these do not yield a complete classification. The requested characterization would extend the connected diagonal result to all planar graphs.