A computer simulation model based on Brownian dynamics is applied to study the diffusion-limited growth of a set of simultaneously formed nuclei on an electrode surface. As the solute electroactive particles are explicitly taken into account, the overlapping of neighbouring diffusion layers and its effects on the process could be analysed. A reaction distance parameter is introduced to correct the discretization error implicit in the simulation method. In the present calculations the time evolution of the reacted charge, the size of the nuclei and the current density were studied. At the same time, the influence of the initial solute concentration and the density of nuclei on these properties was analysed. A parameter named the environmental potential has been defined to characterize the influence of the neighbouring nuclei in the size and growth of any nucleus of the distribution. This parameter shows a clear correlation with the size of the nuclei and allows us to explain the size dispersion observed at each nuclear density. (C) 2004 Elsevier B.V. All rights reserved.