Cumulative distributions of cos(Ψ_star, BH) at different redshifts (upper panel). The black line represents the cumulative distribution of a uniform distribution. In the lower panel, we show additionally show the evolution of the percentage of BHs or BH-galaxy systems that present an alignment angle Ψ_star, BH lower than 45° (red line), 30° (blue line), or 15° (red line). The two vertical dashed lines indicate the epochs where an additional level of refinement was added in the simulation.