  Equitable list arboricity, introduced by Zhang in 2016, generalizes the
notion of equitable list coloring by requiring the subgraph induced by each
color class to be acyclic (instead of edgeless) in addition to the usual upper
bound on the size of each color class. Graph $G$ is equitably $k$-list
arborable if an equitable, arborable list coloring of $G$ exists for every list
assignment for $G$ that associates with each vertex in $G$ a list of $k$
available colors. Zhang conjectured that any graph $G$ is equitably $k$-list
arborable for each $k$ satisfying $k \geq \lceil (1+\Delta(G))/2 \rceil$. We
verify this conjecture for powers of cycles by applying a new lemma which is a
general tool for extending partial equitable, arborable list colorings. We also
propose a stronger version of Zhang's Conjecture for certain connected graphs:
any connected graph $G$ is equitably $k$-list arborable for each $k$ satisfying
$k \geq \lceil \Delta(G)/2 \rceil$ provided $G$ is neither a cycle nor a
complete graph of odd order. We verify this stronger version of Zhang's
Conjecture for powers of paths, 2-degenerate graphs, and certain other graphs.
We also show that if $G$ is equitably $k$-list arborable it does not
necessarily follow that $G$ is equitably $(k+1)$-list arborable which addresses
a question of Drgas-Burchardt, Furmanczyk, and Sidorowicz (2018).
