We use Monte Carlo computer simulation to study the effect of several molecular parameters on controlled/"living" radical polymerization in bulk and on flat substrates. Specifically, we investigate how the molecular weight and molecular weight distribution of grown polymers depend on the initial number of initiators, the initial number of monomers, the initiator activation probability, the initial probability of addition of a new monomer to a growing chain, the probability of terminating two "living" polymers, and the numbers of "living" polymers and their lifetime. Some observations reported here are common to both bulk- and surface-initiated polymerizations. Specifically, we demonstrate that increasing the termination probability and/or decreasing the initial probability of addition of a new monomer to a growing chain broadens the molecular weight distribution. In addition, decreasing the lifetime of the "living" radicals results in polymers with narrower molecular weight distributions. One of the goals of this work is to compare the results of polymerization initiated in bulk with that initiated from flat substrates. Our results reveal that the confinement experienced by the surface-initiated polymers leads to an increased number of early terminations, relative to the bulk- initiated polymerization, which in turn, broadens the molecular weight distribution. This effect is enhanced by increasing the grafting density of the initiators on the surface.