Nuclear magnetic resonance (NMR) spectroscopy is an important molecular characterisation method that may aid the synthesis and production of graphenes, especially the molecular-scale graphene nanoislands that have gathered significant attention due to their potential electronic and optical applications. Herein, carbon-13 NMR chemical shifts were calculated using density functional theory methods for finite, increasing-size fragments of graphene, hydrogenated graphene (graphane) and fluorinated graphene (fluorographene). Both concentric hexagon-shaped (zigzag boundary) and crenellated (armchair) fragments were investigated to gain information on the effect of different types of flake boundaries. Convergence trends of the 13C chemical shift with respect to increasing fragment size and the boundary effects were found and rationalised in terms of low-lying electronically excited states. The results predict characteristic behaviour in the 13C NMR spectra. Particular attention was paid to the features of the signals arising from the central carbon atoms of the fragments, for graphene and crenellated graphene on the one hand and graphane and fluorographene on the other hand, to aid the interpretation of the overall spectral characteristics. In graphene, the central nuclei become more shielded as the system size increases whereas the opposite behaviour is observed for graphane and fluorographene. The 13C signals from some of the perimeter nuclei of the crenellated fragments obtain smaller and larger chemical shift values than central nuclei for graphene and graphane/fluorographene, respectively. The diameter of the graphenic quantum dots with zigzag boundary correlates well with the predicted carbon-13 chemical shift range, thus enabling estimation of the size of the system by NMR spectroscopy. The results provide data of predictive quality for future NMR analysis of the graphene nanoflake materials.