Random subdivisions in a D-dimensional Euclidean space are commonly observed in many scientific fields, such as metallurgy, geology, biology, and even, in the case of large D, in subjects related to information codification. This paper presents an analytical approximation of the size probability distribution in space subdivisions generated by random point processes, which include the well-known cases of the Poisson-Voronoi and the Johnson-Mehl cellular structures. Based on the calculations of Ann. Math. Stat. 33, 958 (1962)] and an assumption for the distribution shape, the cell size distributions are obtained in a general way for a very wide range of random space subdivisions.