We investigate the nature of the relations between black hole (BH) mass (MBH) and the central velocity dispersion (σ) and, for core-Sérsic galaxies, the size of the depleted core (Rb). Our sample of 144 galaxies with dynamically determined MBH encompasses 24 core-Sérsic galaxies, thought to be products of gas-poor mergers, and reliably identified based on high-resolution Hubble Space Telescope imaging. For core-Sérsic galaxies, i.e., combining normal-core (Rb < 0.5 kpc) and large-core galaxies (Rb ≳ 0.5 kpc), we find that MBH correlates remarkably well with Rb such that ${M}_{\mathrm{BH}}\propto {R}_{{\rm{b}}}^{1.20\pm 0.14}$ (rms scatter in log MBH of Δrms ∼ 0.29 dex), confirming previous works on the same galaxies apart from 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 MBH-σ relation MBH ∝ σ4.88±0.29 with Δrms ∼ 0.47 dex; however, at the high-mass end, large-core galaxies (four with measured MBH) are offset upward from this relation by (2.5-4) × σs, explaining the previously reported steepening of the MBH-σ relation for massive galaxies. Large-core spheroids have magnitudes MV ≲ -23.50 mag, half-light radii Re ≳ 10 kpc, and are extremely massive, M* ≳ 1012 M☉. Furthermore, these spheroids tend to host ultramassive BHs (MBH ≳ 1010 M☉) tightly connected with their Rb rather than σ. The less popular MBH-Rb relation exhibits ∼62% less scatter in log MBH than the MBH-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-LV relation observed at MV ≲ -23.5 mag.