Zhang's equitable list arboricity conjecture

Let $G$ be a graph, let $L$ be a $k$-assignment for $G$, and call $G$ equitably $k$-list arborable if there is an arborable $L$-coloring in which every color class has size at most $\lceil |V(G)|/k\rceil$ for every such $L$. Write $\Delta(G)$ for the maximum degree of $G$.

Zhang's conjecture. Any graph $G$ is equitably $k$-list arborable for each $k$ satisfying

$$k\geq \left\lceil\frac{\Delta(G)+1}{2}\right\rceil.$$

The conjecture is a list analogue of the Equitable Vertex Arboricity Conjecture. It has been verified for 2-degenerate graphs, 3-degenerate claw-free graphs with maximum degree at least $4$, planar graphs with maximum degree at least $8$, and grids of dimensions $2$, $3$, and $4$, but remains open in general.