  The distribution function of particles over clusters is proposed for a system
of identical intersecting spheres, the centres of which are uniformly
distributed in space. Consideration is based on the concept of the rank number
of clusters, where the rank is assigned to clusters according to the cluster
sizes. Distribution is universal in the sense that it does not depend on
boundary conditions and is valid for infinite medium. The form of the
distribution function is determined by only one parameter, equal to the ratio
of the sphere radius (`interaction radius') to the average distance between the
centres of the spheres. This parameter plays also a role of the order
parameter. It is revealed under what conditions the universal distribution
behaves like well known log-normal distribution. Applications of the proposed
distribution to some realistic physical situations, which are close to the
conditions of the gas condensation to liquid, are considered.
