We employ a Monte Carlo simulation scheme based on the bond fluctuation model to simulate template polymerization via controlled polymerization scheme involving copolymerization of free monomers (A) and monomers bound to a template (B) that consists of linear or ring-like substrates with equidistant sites occupied by bound B monomers. Both A and B are chemically identical; i.e., there is no interaction potential acting between A and B. A new macromolecule is initiated in bulk by activation of an initiator; any monomer that is within the reaction distance (nearest neighbors) of the initiator can be incorporated into the chain. As the macromolecule grows, it adds either bulk (i.e., A) or template-bound monomers (i.e., B) to its chain. The living nature of the polymers is assured by eliminating any termination or chain transfer. We analyze the effect of the number and spacing of the B bound monomers on the substrate on the chemical composition and monomer distribution in the resultant A-B random copolymer. Our results reveal that the likelihood of B being incorporated in the A-B copolymer increases with increasing the number and density of the B monomers on the template substrate; the maximum sequence length of "polymerized" bound B monomers increases with increasing the number of bound B monomers present in a single substrate. Long consecutive sequences of B bound monomers in the A-B copolymer are formed when the B bound monomers are immobilized in space in high densities.