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The aim of this paper is to discuss the asymptotic properties of the coefficients of generating functions which satisfy a system of functional equations. It turns out that under certain general conditions these coefficients are related to the distribution of a multivariate random variable that is asymptotically normal. As an application it turns out that the distribution of the terminal symbols in context‐free languages is typically asymptotically normal. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10, 103–124 (1997)

Let X n be the number of cuts needed to isolate the root in a random recursive tree with n vertices. We provide a weak convergence result for X n . The basic observation for its proof is that the probability distributions of {X n : n = 2, 3, . . .} are recursively defined by X n d = X n−Dn + 1, n = 2, 3, . . ., X 1 = 0, where D n is a discrete random variable with. . , n−1, which is independent of (X 2 , . . . , X n ). This distributional recursion was not studied previously in the sense of weak convergence.