Redshift evolution of the total and mean BH masses and BHARs, averaged over 29 independent merger trees. Shaded areas are 1σ dispersions. Top, left panel: total BH mass (summed over all BH progenitors at each redshift in each simulation, black line) and the BH mass grown by means of sub-Eddington (magenta line) and super-Eddington (cyan line) accretion events. Top, right panel: total BHAR (black line) and BHAR obtained considering only sub- (magenta line) and super- (cyan line) Eddington accreting BHs. The mean BH mass and BHAR (averaged over all BH progenitors at each redshift in each simulation) are shown in the bottom panels (left and right, respectively).