In this paper we presented a solution for the simulation of random distributions of points on surfaces. In particular the proposed algorithms are suitable to simulate a large variety of situations which are typical in spatial data analysis.These procedures can be applied to generate still more complex structures of randomness. For instance, if we want to simulate a distribution of trees in a forest where the mean number of items per unity of surface area depends not only on biological species, but also on their age and on reciprocal distance, an approach of this kind is plenty satisfactory, and leads to a complete solution of the simulation problem.
