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Applications of graph colouring often involve taking restrictions intoaccount, and it is desirable to have multiple (disjoint) solutions. In theoptimal case, where there is a partition into disjoint colourings, we speak ofa packing. However, even for complete bipartite graphs, the list chromaticnumber can be arbitrarily large, and its exact determination is generallydifficult. For the packing variant, this question becomes even harder.  In this paper, we study the correspondence- and list packing numbers of(asymmetric) complete bipartite graphs. In the most asymmetric cases, Latinsquares come into play. Our results show that every $z \in \mathbb Z^+\setminus {3}$ can be equal to the correspondence packing number of a graph.Additionally, we disprove a recent conjecture that relates the list packingnumber and the list flexibility number.

Packing colourings in complete bipartite graphs and the inverse problem for correspondence packing