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We present new, exceptionally efficient proofs of Poisson--Dirichlet limittheorems for the scaled sizes of irreducible components of random elements inthe classic combinatorial contexts of arbitrary assemblies, multisets, andselections, when the components generating functions satisfy certain standardhypotheses. The proofs exploit a new criterion for Poisson--Dirichlet limits,originally designed for rapid proofs of Billingsley's theorem on the scaledsizes of log prime factors of random integers (and some new generalizations).  Unexpectedly, the technique applies in the present combinatorial setting aswell, giving, perhaps, a long sought-after unifying point of view. The proofsdepend also on formulas of Arratia and Tavar{\'e} for the mixed moments ofcounts of components of various sizes, as well as formulas of Flajolet andSoria for the asymptotics of generating function coefficients.

Poisson--Dirichlet Limit Theorems in Combinatorial Applications via Multi-Intensities