  We investigate the list packing number of a graph, the least $k$ such that
there are always $k$ disjoint proper list-colourings whenever we have lists all
of size $k$ associated to the vertices. We are curious how the behaviour of the
list packing number contrasts with that of the list chromatic number,
particularly in the context of bounded degree graphs. The main question we
pursue is whether every graph with maximum degree $\Delta$ has list packing
number at most $\Delta+1$. Our results highlight the subtleties of list packing
and the barriers to, for example, pursuing a Brooks'-type theorem for the list
packing number.
