  We present a probabilistic approach to the core-size in random maps, which
yields straightforward and singularity analysis-free proofs of some results of
Banderier, Flajolet, Schaeffer and Soria. The proof also yields convergence in
distribution of the rescaled size of the k'th largest 2-connected block in a
large random map, for any fixed k > 1, to a Fr\'echet-type extreme order
statistic. This seems to be a new result even when k=2.
