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Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structure and the asymptotics of the first and second moments of the sequence. In particular, a generaldoi:10.1214/aoap/1075828056 fatcat:ug7ixpmlwfgcfk4cfmt7gos7ha