Distribution of host stellar mass, BH mass, specific star formation rate, BH Eddington ratio, BH spin, and BH mass ratio as a function of redshift for numerical mergers (blue points), delayed mergers (green points), and the global population of main BHs, matched to the M_* distribution of numerical mergers by a factor pdf_NM(log₁₀M_*)/pdf_all(log₁₀M_*) (red log-scaled hexagonal bins). For numerical mergers, we show the spin of the primary in the snapshot prior to the merger. For delayed mergers, the mass ratio refers to the pre-numerical merger mass ratio since the final mass ratio cannot be obtained from the simulation. The main BH population is matched to the M_* distribution of numerical mergers for each redshift bin. In each bin, the geometric average of numerical mergers, delayed mergers, and mass-weighted main BHs is represented with solid lines, with their standard errors shown in the shaded regions.