Different models of spatial arrangement (general random closed sets, union sets of processes of particles with given probabilistic distributions of shape, side and position as well as space-filling cells) are examined. The results covering random non-interacting (overlapping) systems, random clusters, uniform systems of particles (lattices of bodies), uniform systems with faults (vacancies, interstitials, vacancy - interstitial pairs, foreign particles) are given and documented by numerous graphs. The general treatment of the problem allows the application of the results to linear, planar as well as spatial systems. Statistics of planar cases (sections), estimation of model parameters and stereological applications are covered in a special section.