We investigate the nature of the relations between black hole (BH) mass (M BH ) and the central velocity dispersion (σ) and, for core-Sérsic galaxies, the size of the depleted core (R b ). Our sample of 144 galaxies with dynamically determined M BH encompasses 24 core-Sérsic galaxies, thought to be products of gas-poor mergers, and reliably identified based on high-resolution HST imaging. For core-Sérsic galaxies-i.e., combining normal-core (R b < 0.5 kpc) and large-core galaxies (R b 0.5 kpc), we find that M BH correlates remarkably well with R b such that M BH ∝ R 1.20±0.14 b (rms scatter in log M BH of ∆ rms ∼ 0.29 dex), confirming previous works on the same galaxies except three new ones. Separating the sample into Sérsic, normal-core and large-core galaxies, we find that Sérsic and normal-core galaxies jointly define a single log-linear M BH − σ relation M BH ∝ σ 4.88±0.29 with ∆ rms ∼ 0.47 dex, however, at the high-mass end large-core galaxies (four with measured M BH ) are offset upward from this relation by (2.5 − 4) × σ s , explaining the previously reported steepening of the M BH − σ relation for massive galaxies. Large-core spheroids have magnitudes M V −23.50 mag, half-light radii R e 10 kpc and are extremely massive M * 10 12 M ⊙ . Furthermore, these spheroids tend to host ultramassive BHs (M BH 10 10 M ⊙ ) tightly connected with their R b rather than σ. The less popular M BH − R b relation exhibits ∼ 62% less scatter in log M BH than the M BH − σ relations. Our findings suggest that large-core spheroids form via multiple major 'dry' merger events involving super/ultramassive BHs, consistent with the flattening of the σ − L V relation observed at M V −23.5 mag.