Universal distributions generated in a nucleation pulse

Asymptotic analysis of the nucleation-growth equations describing a nucleation pulse of arbitrary duration is performed. It is discovered that after extended growth an asymptotic distribution is established, which is not of any standard form (Gauss, log-normal, etc.). Regardless of the mass exchange mechanism between the nucleus and the metastable phase, in the extremes of long and short pulses the shapes of the distribution become universal, with additional insensitivity of either the maximum or, respectively, the width to the duration of the pulse.