We have developed a reactive molecular dynamics (RMD) scheme to simulate irreversible polymerization of realistic polymer systems in a coarse-grained resolution. We have studied the chain propagation of styrene to polystyrene. For monodisperse polystyrene samples, we reproduce the results of equilibrium MD simulations: density, end-to-end distance, radius of gyration, and different geometrical distribution functions. The RMD simulations on polydisperse systems should be considered as case studies intended to understand the influence of different tuning parameters of the RMD approach on calculated polymer quantities. The parameters for the irreversible polymerization include the number and position of the initiator units (1*) as well as capture radii r(1) (r(P)) defining the geometrical conditions for chain initiation (propagation) and a characteristic delay time tau(r) separating two reactive MD time steps. As a function of the r(1) (r(P)) and tau(r), it is possible to model polymerization processes both in the limit of almost unrelaxed and fully relaxed samples. The strong influence of the spatial localization of the 1* on the polymer size distribution is discussed in detail. The RMD results are used to formulate optimized computational conditions for the simulation of irreversible polymerizations, to explain observed trends in the polydispersity index, and to suggest experiments that might lead to an unexpected polymer size distribution.