Statistical analysis of a few key properties of the accretion episodes occurred in the Box4 run. The entire set of accretion episodes occurred during the simulation has been considered (i.e. for every BH and at every redshift). The top (middle) panel shows a 2D histogram of the values of J_d/J_BH (θ_BH−d) as a function of mass. Each bin is colour-coded by the number of accretion episodes in that bin (N_bin), normalised to the total number of episodes per mass bin (N_{mass bin}). In the top panel, the dashed line pinpoints $J_{\text{d}}/J_{\text{BH}}\propto M_{\text{BH}}^{-37/45}$ (for the self-gravitating case, Eq. (23)); the dotted line shows $J_{\text{d}}/J_{\text{BH}}\propto M_{\text{BH}}^{23/16}$ (non-self-gravitating case, Eq. (19)). a = 0.998 and f_Edd = 1 are assumed to plot these reference lines. The bottom panel shows the fraction of counter-rotating accretion episodes over the total, per BH mass bin.