The experimentally determined zero-shear viscosity of entangled branched polymers shows dramatic variation due to the topological arrangements of the branches in branched polymer melts. The position of the branch points, the arm length, and number of the arms are essential to defining the rheological behavior. Recent advances in molecular tube models have led to a much greater understanding of the linear rheology of linear, star, H-shaped, pom-pom, and comb polymers. We correct and extend existing molecular theories for the linear viscoelasticity of comb polymer melts, especially in accounting for (1) polydispersity and (2) the path length of backbone extremities. We compare the predictions with linear rheological data of nearly monodisperse polybutadiene combs. We then predict the zero-shear viscosity for monodisperse comb polyethylenes with varying arm lengths, backbone lengths, and number of arms. For a fixed molecular weight, we find that combs with the longest arms but few branch points give the highest predicted zero-shear viscosities and that they obey an exponential dependence on the length of the arms in the same way as star polymers. We find that combs with short arms, under four entanglements, lie below the 3.4 power law obeyed by linear polymers. All other comb topologies are bounded by these extremes.