Equitable list point arboricity of graphs

A graph G is list point k-arborable if, whenever we are given a k-list assignment L(v) of colors for each vertex v ∈ V(G), we can choose a color c(v) ∈ L(v) for each vertex v so that each color class induces an acyclic subgraph of G, and is equitable list point k-arborable if G is list point k-arborable and each color appears on at most ⌈|V(G)|/k⌉ vertices of G. In this paper, we conjecture that every graph G is equitable list point k-arborable for every k ≥ ⌈(∆(G)+1)/2⌉ and settle this for complete graphs, 2-degenerate graphs, 3-degenerate claw-free graphs with maximum degree at least 4, and planar graphs with maximum degree at least 8.