Graphitic carbon nitride (g-C3N4) has garnered much attention due to its potential as an efficient metal-free photocatalyst. This study examines the evolution of properties in zero-dimensional quantum dots up to sizable clusters that mimic extended g-C3N4 monolayers. We employ density functional theory to investigate systematically the structural, electronic, and optical properties of the g-C3N4-based melamine and heptazine building blocks using a "bottom-up" construction of polymeric monolayers. The results from our computations indicate that the melamine- and heptazine-based polymeric g-C3N4 systems must be reduced to at least 2.74 and 4.00 nm, respectively, to observe an increase of its optical gap with a size reduction. The present study also examines the nature of the electronic transitions exhibited by g-C3N4-based monolayers through full natural transition orbital and density of state analyses. The most promising sites for water splitting and subsequent chemical doping studies are identified, which generally correspond to the nitrogen and carbon atoms, respectively.