The irreversible polymerization of a monomer liquid has been studied by molecular-dynamics simulation in two and three dimensions. The growth process is studied under good solvent conditions in the dilute regime and up to semidilute and concentrated regimes. In the dilute regime we observe a reaction limitation due to trapping of the growing centers, which is more pronounced in the lower dimension. At higher concentrations the presence of other chains decreases the monomer mobility and reaction rate. Conformational properties are studied by scaling analysis of end-to-end and gyration radii. A crossover from swollen conformations towards screened conformations is observed as growth proceeds.