The polydispersity index, the molecular weight distribution (MWD), and the degree of branching (<(DB)over bar>) are calculated for hyperbranched polymers obtained in self-condensing vinyl polymerization of AB* monomers in the presence of a core-forming molecule (i.e. a multifunctional initiator, B-f*). Two cases are considered : (a) batch polymerization, i.e., with all components mixed together; (b) semibatch polymerization, i.e., slow addition of the monomer to the core-forming molecule. The results obtained for the latter case are also valid for polycondensation of AB(2) monomers. The presence of core-forming molecules leads to a considerable narrowing of the MWD＇s, the polydispersity index decreasing with increasing initiator functionality, f. In the batch process, we find (P) over bar(w)/(P) over bar(n) approximate to 1 + (P) over bar(n)/f(2) and in the semibatch mode (P) over bar(w)/(P) over bar(n) approximate to 1 + 1/f. The degree of branching obtained in semibatch mode approaches <(DB)over bar> = 2/3, which is higher than for the synthesis using a batch process with or without initiator. The polymers resulting from semibatch mode are predicted to consist of highly branched cores, while the outer parts of the molecules contain the majority of the functional groups. Thus, they are closer to dendrimers than the polymers obtained in batch mode.