The set of kinetic differential equations for star-coupling of polymers have been solved rigorously both with and without the effect of steric hindrance. The relations between the molecular parameters of star-branched polymers and those of prepolymers are derived. When the star-coupling reaction goes quantitatively to completion, the same theoretical result was obtained, no matter whether there is steric hindrance or not. In this case, the more arms in the star-branched polymer, the more homogeneous is the molecular weight distribution; if the number of arms is large enough, the molecular weight distribution will become very narrow and almost be independent of the polydispersity of the arms.