A simple model has been developed to investigate the differences between 2D and 3D diffusion-controlled polymerization kinetics. Besides the different analytical structure of 2D and 3D diffusion equation, the model takes into account the dynamics of the polymer chemically reacting end and the restricted motion of the diffusing monomers in a growing polymer network. These effects are strongly related to the dimensionality of the system and may contribute to modulate the polymerization rate. Theoretical considerations suggest different behavior when 2D polymerization takes place in a poor solvent, whereas minor differences should be present in good solvents and 3D systems.