  We prove a general multi-dimensional central limit theorem for the expected
number of vertices of a given degree in the family of planar maps whose vertex
degrees are restricted to an arbitrary (finite or infinite) set of positive
integers D. Our results rely on a classical bijection with mobiles (objects
exhibiting a tree structure), combined with refined analytic tools to deal with
the systems of equations on infinite variables that arise. We also discuss some
possible extension to maps of higher genus.
