Ultramassive black holes in the most massive galaxies: $M_{\rm BH}-\sigma$ versus $M_{\rm BH}-R_{\rm b}$

[Abridged] We investigate the nature of the relations between black hole (BH) mass ($M_{\rm BH}$) and the central velocity dispersion ($\sigma$) and, for core-S\'ersic galaxies, the size of the depleted core ($R_{\rm b}$). Our sample of 144 galaxies with dynamically determined $M_{\rm BH}$ encompasses 24 core-S\'ersic galaxies, thought to be products of gas-poor mergers, and reliably identified based on high-resolution HST imaging. For core-S\'ersic galaxies -- i.e., combining normal-core ($R_{\rm b} $ 10 kpc and are extremely massive $M_{*} \ge 10^{12}M_{\odot}$. Furthermore, these spheroids tend to host ultramassive BHs ($M_{\rm BH} \ge 10^{10}M_{\odot}$) tightly connected with their $R_{\rm b}$ rather than $\sigma$. The less popular $M_{\rm BH}-R_{\rm b}$ relation exhibits $\sim$ 62% less scatter in log $M_{\rm BH}$ than the $M_{\rm BH}- \sigma$ relations.