  Applications of graph colouring often involve taking restrictions into
account, and it is desirable to have multiple (disjoint) solutions. In the
optimal case, where there is a partition into disjoint colourings, we speak of
a packing. However, even for complete bipartite graphs, the list chromatic
number can be arbitrarily large, and its exact determination is generally
difficult. 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, Latin
squares 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 packing
number and the list flexibility number.
