The number of components in a logarithmic combinatorial structure

Under very mild conditions, we prove that the number of components in a dec omposable logarithmic combinatorial structure has a distribution which is c lose to Poisson in total variation. The conditions are satisfied for all as semblies, multisets and selections in the logarithmic class. The error in t he Poisson approximation is shown under marginally more restrictive conditi ons to be of exact order O(1/ log n), by exhibiting the penultimate asympto tic approximation; similar results have previously been obtained by Hwang [ 20], under stronger assumptions. Our method is entirely probabilistic, and the conditions can readily be verified in practice.