  Catalytic equations appear in several combinatorial applications, most
notably in the numeration of lattice path and in the enumeration of planar
maps. The main purpose of this paper is to show that the asymptotic estimate
for the coefficients of the solutions of (so-called) positive catalytic
equations has a universal asymptotic behavior. In particular, this provides a
rationale why the number of maps of size $n$ in various planar map classes
grows asymptotically like $c\cdot n^{-5/2} \gamma^n$, for suitable positive
constants $c$ and $\gamma$. Essentially we have to distinguish between linear
catalytic equations (where the subexponential growth is $n^{-3/2}$) and
non-linear catalytic equations (where we have $n^{-5/2}$ as in planar maps).
Furthermore we provide a quite general central limit theorem for parameters
that can be encoded by catalytic functional equations, even when they are not
positive.
