Correlation of cos(Ψ_star, BH) against the BH mass (for the primary BH with a mass greater than 2 × 10⁴ M_⊙; left panels) and the BH spin magnitude (right panels), with color coding according to the percentage of mass gain through BH-merger f_BH, merger at each specific redshift. At z = 3, most BHs whose mass is close to their seed mass (∼[1 − 3]×10⁴ M_⊙) are still in the process of spinning up through early gas accretion (i.e., blue filled circles). Their dimensionless spin parameters are close to unity, and tend to be aligned with the stellar component angular momentum. Other BHs have already undergone major mergers (red and green filled circles) which tend to decrease the magnitude of their spin while increasing the scatter in the distribution of cos(Ψ_star, BH). At low redshift, the same trend is observed in the cos(Ψ_star, BH)–|a| diagram. The corresponding correlations between |a| and the BH mass can be directly seen in Fig. 23 of Dubois et al. (2021).