  A $k$-uniform hypergraph (or $k$-graph) $H = (V, E)$ is $k$-partite if $V$
can be partitioned into $k$ sets $V_1, \ldots, V_k$ such that each edge in $E$
contains precisely one vertex from each $V_i$. In this note, we consider list
colorings for such hypergraphs. We show that for any $\epsilon > 0$ if each
vertex $v \in V(H)$ is assigned a list of size $|L(v)| \geq
\left((k-1+\epsilon)\Delta/\log \Delta\right)^{1/(k-1)}$, then $H$ admits a
proper $L$-coloring, provided $\Delta$ is sufficiently large. Up to a constant
factor, this matches the bound on the chromatic number of simple $k$-graphs
shown by Frieze and Mubayi, and that on the list chromatic number of triangle
free $k$-graphs shown by Li and Postle. Our results hold in the more general
setting of "color-degree" as has been considered for graphs. Furthermore, we
establish a number of asymmetric statements matching results of Alon, Cambie,
and Kang for bipartite graphs.
