Limits of logarithmic combinatorial, structures

Under very mild conditions, we prove that the limiting behavior of the comp onent counts in a decomposable logarithmic combinatorial structure conforms to a single, unified pattern, which includes functional central limit theo rems, Erdas-Turan laws, Poisson-Dirichlet limits for the large components a nd Poisson approximation in total variation for the total number of compone nts. Our approach is entirely probabilistic, and the conditions can readily be verified in practice.