A ternary self-condensing vinyl polymerization(SCVP) system consisting of monomers, inimers and core initiators is studied by the principle of statistical mechanics. Starting from partition functions for polymerization that constructed from two different viewpoints, explicit expressions of the size distribution function(SDF), equilibrium free energy, and the law of mass action are obtained. For two types of hyperbranched polymers(HBPs) formed in the system, the first, the second, and the third mean-square radii of gyration(MSRG) are presented under various conditions. Furthermore, the solvent effect and excluded volume effect are taken into account in the calculation of the MSRG. With these results, the effects of monomers, inimers and core initiators on the spatial dimension of HBPs are discussed. It is shown that the competition between polymers with and without a core in the growing process results in a significant influence on the average properties of the system. Starting from partition functions for polymerization that constructed from two different viewpoints, explicit expressions of the size distribution function (SDF For two types of hyperbranched polymers (HBPs) formed in the system, the first, the second, and the third mean-square radii of gyration (MSRG) are presented under Various conditions. Furthermore, the solvent effect and excluded volume effect are taken into account in the calculation of the MSRG. With these results, the effects of monomers, inimers and core initiators on the spatial dimension of HBPs are discussed. competition between polymers with and without a core in the growing process results in a significant influence on the average properties of the system.