Distribution of host galaxy stellar mass (left panel), BH mass (middle panel), and Eddington ratio (right panel), for delayed merger remnants, in green, numerical merger remnants, in blue, and for the global main BH population, in orange, at redshift 3.5 < z < 4. For M_• and f_Edd, we also show in red the global main BH distributions weighted by a factor pdf_NM(log₁₀M_*)/pdf_all(log₁₀M_*), where pdf_NM(log₁₀M_*) and pdf_all(log₁₀M_*) are respectively the distribution of log₁₀M_* for numerical merger remnants and all galaxies, as shown in the left panel. In this way, we build a sample of the global main BHs population that matches the M_* distribution of merging BHs. Merging BHs have similar properties when compared to a sample matched in M_*, but have higher masses and Eddington ratios when compared to the full population of BHs.