Monte Carlo simulations were performed on star-burst dendrimer molecules having various numbers of spacer bonds P and various numbers of generations g. Each molecule is modeled by connecting freely-rotating rigid bonds in a star-burst architecture and by attaching to each end of the bond a hardsphere bead of diameter d. Dependence of the mean square end-center distance and the mean square monomer-center distance on P, g, and d were each found to follow st power-law scaling behavior in P for fixed g and small d. The results show that the scaling exponent nu for star-burst dendrimers has the same Value as that of linear polymers. For different generations g, the asymptotic regime in which the scaling behavior is valid was found to be quite different. In the scaling regime, our results show that the size of dendrimers follows the scaling law (Pg)N-1-nu(2 nu-1), where N is the total number of monomers in a star-burst molecule. We also discuss physical properties in the high-concentration regime, where the scaling law is no longer valid.