An explicit theoretical expression is derived for the distribution of the stationary nucleation rate around a growing stable cluster of the new phase. The theoretical formula obtained is used in a computer simulation of instantaneous and progressive nucleation which is performed without recourse to the concept of nucleation exclusion zones. The simulated spatial distributions of nuclei are analysed and compared with the theoretical distribution function of the distances between nth neighbours. Deviations of the simulated spatial distributions from the random distributions are detected, in qualitative agreement with experimental findings.