Metallic or semiconductor nanocrystals produced by very different techniques often display size distributions whose limiting shape (e.g., after long annealing times) is self-preserving and close to lognormal. We briefly survey the diverse microscopic mechanisms leading to this behavior, and present an experimental study of its inception in the case of semiconducting nanocrystals synthesized by ion implantation in silica. This example shows how the ultimate lognormal distribution is related to the system's memory loss of initial nucleation and growth processes.