Good control on molecular properties, and as a consequence on end-use properties, is very important for low-density polyethylene (LDPE) manufacturers. However, the connection between the architecture of polymer chains and the kinetic mechanism and polymerization conditions is still a subject of study. In this work, we present a comprehensive model of the polymerization of ethylene in high-pressure tubular reactors. In addition to the usual predictions of conversion, temperature profiles, and average molecular properties, this model also provides bivariate distributions such as molecular-weight-long-chain branching distribution and molecular-weight-short-chain branching distribution of LDPE produced under different operating conditions. The 2D probability-generating function technique is applied to obtain the bivariate distributions. This is a deterministic technique that allows the calculation of the distributions without any prior assumption of their shape.