We have designed a GaAs based structure in which the influence of the initial supersaturation of solute atoms, here As, on the nucleation and conservative growth of a precipitate phase during annealing can be studied. Size distributions and densities were extracted from transmission electron microscopy images under well defined and appropriate conditions, and the volume fraction that the precipitate phase occupies was deduced from these measurements for a variety of experimental conditions. We show that in the 0.06%–0.5% supersaturation range, the mean size of the precipitates obtained after annealing does not depend on the initial supersaturation of As atoms. On the other hand, the density of precipitates is proportional to this supersaturation. However, we observe that the increase of the precipitate volume fraction leads to a considerable broadening of the precipitate size distributions. The size invariance revealed here suggests that, for a volume fraction of less than 1%, the populations are in quasiequilibrium with the supersaturated matrix and that the growth is driven by the interchange of As atoms (and vacancies) between the precipitates and the matrix and not directly from one precipitate to the next. It can be inferred that the diffusion fields surrounding the precipitates do not overlap much during the growth although some deviation from the expected shape of the size distribution may reveal the limitations of the nonlocal mean-field approximation suggested here.