  We study the local limits of uniform high genus bipartite maps with
prescribed face degrees. We prove the convergence towards a family of infinite
maps of the plane, the q-IBPMs, which exhibit both a spatial Markov property
and a hyperbolic behaviour. Therefore, we observe a similar local behaviour for
a wide class of models of random high genus maps, which can be seen as a result
of universality. Our results cover all the regimes where the expected degree of
the root face remains finite in the limit. This follows a work by the same
authors on high genus triangulations arXiv:1902.00492.
