Variations of the BH mass vs the galaxy mass with color coding according to the value of cos(Ψ_star, BH). We show three typical evolutions of intermediate mass BHs to illustrate the three different regimes followed by the variations of Ψ_star, BH: (1) a tendency to BH-galaxy spin alignment right after their birth and for relatively short periods (M_BH < 3 × 10⁴ M_⊙ and M_star ≲ 2 × 10⁷ M_⊙), (2) erratic variations (M_BH ≲ 10⁵ M_⊙), (3) new tendency to alignment at late time (5 × 10⁹ M_⊙ ≲ M_star). Note that in the case of BH-1049, the blue region at late time corresponds to the BH spin anti-alignment situation.