The effects of nearest neighbours on the local nucleation rates and on the spatial distribution of electrodeposited nuclei growing under diffusion control have been analysed. Based upon the Dirichlet tessellation procedure, a systematic criterion is developed for selecting for each site on the surface its natural neighbours, i.e. those nuclei whose diffusional fields are not screened by other nuclei. Through computer simulations, the combined effect of the natural neighbours on the local nucleation rate at a site, or that of only the most influential neighbour, as well as the resulting spatial distributions of nuclei, are analysed. Comparison with experimental results shows that the effect of the most influential neighbour determines the spatial distribution of nuclei. It is also shown that the spatial distribution of nuclei does not depend on the detailed dependence of the local nucleation rate on the radial distance to its most influential or natural neighbours, as long as their propagation occurs with the same time-dependence.