Panel a: the black hole mass as a function of the dynamical mass of WISSH QSOs (cyan symbols), compared with z ∼ 2−6, luminous QSOs from literature, as indicated in the legend (see text for details). The total dynamical mass associated with the QSO + companion galaxies with measured M_dyn are also shown by the empty symbols. For WISSH QSOs and companions (as most literature sources), M_dyn values are based on the FWHM of the CO or [CII] emission lines. The M_BH − M_dyn relation found for local galaxies by Jiang et al. (2011) is also indicated by the dashed line, with the associated 0.4 dex intrinsic scatter (shaded region). Panel b: molecular gas fraction (corrected for the dependence on redshift and offset from main-sequence) as a function of the host-galaxy stellar mass for WISSH QSOs and a compilation of high-z QSOs and local AGN (see text). WISSH QSOs with dust-based M_gas are indicated by orange stars. The average f_gas − M_* relation found for z <  4 star-forming galaxies from the PHIBSS survey (Tacconi et al. 2018) is shown by the solid line.