Supermassive BH mass (left) and BH-to-stellar mass ratio (right) as a function of redshift for z_ffb​ = ​9 (blue) and 12 (magenta), with m​ = ​10⁴ M_⊙. This is either in a hot disk (Eq. (19), solid) or in a cold disk (Eq. (21), long-dashed). The FFB-threshold halo properties as a function of z_ffb are from Eqs. (24) and (25) (Dekel et al. 2023a). The SFE is ϵ​ = ​0.2. The BHs are assumed to be on circular orbits responding to DF from the stellar disk (V/σ​ = ​5) plus an NFW DM halo (whose contribution is negligible, short dashed). The BHs are assumed to start in an exponential disk whose radius is estimated in Eq. (27) (Li et al. 2024b). The galaxy stellar mass, assumed to be constant in time, is marked (dotted). The 1σ scatter due to the scatter in disk size in Eq. (27) is ±0.2 dex. Eddington growth is marked for comparison (thin dashed green) The observational estimates are shown for comparison. The data are from Maiolino et al. (2024b) (circles), Harikane et al. (2023) and Übler et al. (2023) (squares). The selection-bias-corrected mean and standard deviation by (Pacucci et al. 2023) based on the data in red symbols are marked by the red lines. The values of f_bh at z​ = ​4 − 7 are > 3σ above the standard z​ = ​0 low-z ratio by Reines & Volonteri (2015) (indicated by dashed green lines). The average SMBH masses and f_bh ratios as deduced from the observations at z​ ∼ ​4 − 7 are reproduced by the 10⁴ M_⊙ seeds of the FFB scenario.