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We examine the influence of dimer mobility on the size distribution of two-dimensional islands formed by irreversible nucleation and growth during deposition. We first characterize the transition in scaling of the mean island density with increasing dimer mobility, from the classic form described by Venables [Philos. Mag. 27, 697 (1973)] to the modified form for "rapid" mobility described by Villain et al. [ J. Phys. (France)doi:10.1103/physrevb.53.4099 pmid:9983966 fatcat:olledi63y5bo5i6m4h5mdsun5u