  The main goal of this paper is to determine the asymptotic behavior of the
number $X_n$ of cut-vertices in random planar maps with $n$ edges. It is shown
that $X_n/n \to c$ in probability (for some explicit $c>0$). For so-called
subcritical classes of planar maps (like outerplanar maps) we obtain a central
limit theorem, too. Interestingly the combinatorics behind this seemingly
simple problem is quite involved.
