Spin alignment process in the idealised Milky Way galaxy. Top panels: angle subtended by the BH angular momentum and the z-axis θ_r. Bottom panels: BH spin parameter a. Quantities are plotted as a function of time (left panels) and of the ratio between accreted and initial BH mass M_BH/M_BH,0 (right). Each line represents one simulation of the set summarised in Table 1. Dotted lines represent the instant after which condition (6) is no longer satisfied.