Summary of properties related to the most massive BH in the DFROGIN run, as they evolve across time. From top to bottom: z-component of the BH spin direction j_BH,z (black, solid line) and direction of the angular momentum of the gas in the BH kernel j_g,z (orange, dashed line); cosine of the angle between the accretion disc and the BH spin at the beginning of each accretion episode cos θ_BH–d (i.e. left-hand side of Eq. (6), black solid line) and − J_d/(2J_BH) (i.e. right-hand side of Eq. (6), orange dashed line); ratio of the magnitudes of the disc and BH angular momenta J_d/J_BH; BH dimensionless spin parameter α; radiative efficiency of the accretion disc є_r; Eddington ratio f_Edd; BH mass M_BH.