  The paper considers a particular family of set--valued stochastic processes
modeling birth--and--growth processes. The proposed setting allows us to
investigate the nucleation and the growth processes. A decomposition theorem is
established to characterize the nucleation and the growth. As a consequence,
different consistent set--valued estimators are studied for growth process.
Moreover, the nucleation process is studied via the hitting function, and a
consistent estimator of the nucleation hitting function is derived.
