It has usually been assumed that nucleation phenomena are random in space and time; however, spatial and time randomness are not distinguishable in general. The special case of the electrocrystallization of silver on perfect single crystal substrates allows the spatial and time statistics to be distinguished under conditions where elementary events can be separately observed[1–5]. Appropriate models can therefore be tested successively in space and time and then extrapolated to conditions where indistinguishability predominates[6–8]. The development and application of these models are discussed in this paper.