The self-condensing vinyl polymerization system consisting of inimers and multifunctional core initiators is studied by the principle of statistical mechanics. From viewpoints of functional groups and polymers, two types of canonical partition functions are constructed and further are proved to be consistent with each other. In this way, the explicit expressions of equilibrium free energy and law of mass action concerning the polymerization are obtained, and then the equilibrium size distribution functions of hyperbranched polymers are given. With the help of the size distribution functions, the k-th mean square radii of gyration of hyperbranched polymers with and without a core are derived, respectively. In order to investigate the effect of core initiators on the statistical properties of the system, the number and functionality of core initiators have been explicitly taken into account, and the variations of relevant physical quantities against the conversion of vinyl groups under various conditions are presented. It is shown that the presence of core initiator results in a significant influence on average properties of the system, which can be explained from the competition between polymers with and those without a core initiator in their growth process. (C) 2010 Elsevier Ltd. All rights reserved.