Grafting one type polymer onto a different polymer type may yield a comb-branched copolymer. The branching density has a significant effect on its overall molecular weight distribution. A general model is derived to describe the bivariate distribution of molecular weight and branching density for such comb copolymers. The model is applicable for various grafting mechanisms provided the side chains are randomly grafted onto the backbone. The determining parameters are the molecular weight distributions of backbone and side chains, and the branching density. Analytical expressions are obtained for the cases of the side chains having uniform and Schulz-Zimm distributions.