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 δ has list packing number at most δ +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.

List coloring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list-coloring, we seek many in parallel. Our explorations have uncovered a potentially rich seam of interesting problems spanning chromatic graph theory. Given a (Formula presented.) -list-assignment (Formula presented.) of a graph (Formula presented.), which is the assignment of a list (Formula presented.) of (Formula presented.) colors to each vertex (Formula presented.), we study the existence of (Formula presented.) pairwise-disjoint proper colorings of (Formula presented.) using colors from these lists. We may refer to this as a list-packing. Using a mix of combinatorial and probabilistic methods, we set out some basic upper bounds on the smallest (Formula presented.) for which such a list-packing is always guaranteed, in terms of the number of vertices, the degeneracy, the maximum degree, or the (list) chromatic number of (Formula presented.). (The reader might already find it interesting that such a minimal (Formula presented.) is well defined.) We also pursue a more focused study of the case when (Formula presented.) is a bipartite graph. Our results do not yet rule out the tantalising prospect that the minimal (Formula presented.) above is not too much larger than the list chromatic number. Our study has taken inspiration from study of the strong chromatic number, and we also explore generalizations of the problem above in the same spirit.