Experiments in our group have demonstrated the ability to hydrogenate fullerenes, carbon nanotubes and even nanoonions using a polyamine reagent. Because the hydrogenated forms of nanostructured carbon may prove useful for several applications including lightweight, high strength composites containing well dispersed CNTs, advanced materials for space radiation shielding and hydrogen storage in fuel-cells, we seek a greater theoretical understanding of their structures and stabilities. For example, recent experimental work suggests that small fullerenes may be exhaustively hydrogenated using polyamine chemistry but the hydrogenation process becomes decreasingly favored as the fullerenes become larger and larger. Given the current scarcity of giant fullerenes, a thorough experimental exploration of this phenomenon is impractical. In this study, DFT calculations are performed on a variety of large and giant fullerenes (C70-C126) along with three hydrogenated derivatives for each parent fullerene. Geometry optimizations were carried out using PM3 semi-empirical theory. Energies were calculated using B3LYP/6-31G**. The energies of hydrogenation are plotted both as a function of average dihedral angles and degrees of pyramidalization which are measures of the curvature of the fullerene surface. The computational results from this study appear consistent with experimental evidence.