A quantitative study of the structure and electronic properties of Co-corrole, Co-corrin. and Co-porphyrin, using density functional theory, is reported. The structure of each macrocycle is optimized, with no symmetry constraints, by considering different spin states. The ground-state structures and spin states (S = 1 for Co-corrole, S = 0 for Co-corrin and S = 1/2 for Co-porphyrin) are in good agreement with the experimental data available. The trends in the sizes of the coordination cavities upon varying the inner metal atom and/or the macrocycle are analyzed and compared with those for the Fe-porphyrin we studied previously. Our results reveal that most of the distortion of the Co-corrin core in the B-12. coenzyme is due to the inherent properties of Co-corrin. Quite different behaviors are found between corrinoids and porphyrins upon varying the spin state. While an increase in the metal-nitrogen (M-N) distance with spin state occurs in the porphyrins, the corrinoids show little variation in the M-N distance and, in some cases, undergo small structural changes in the ring structure. These results aid in understanding the often discussed question of why nature has chosen corrin/porphyrin for carrying out the particular biological functions identified in the B-12 coenzyme.