  We consider random rooted maps without regard to their genus, with fixed
large number of edges, and address the problem of limiting distributions for
six different parameters: vertices, leaves, loops, root edges, root isthmus,
and root vertex degree. Each of these leads to a different limiting
distribution, varying from (discrete) geometric and Poisson distributions to
different continuous ones: Beta, normal, uniform, and an unusual distribution
whose moments are characterised by a recursive triangular array.
