Evolution of the accretion rate and black hole parameters including and excluding self-gravity plotted by the thick and thin curves, respectively. The top panels refer to the initial black hole spin parameter A₀ = 0.85 while the bottom panels correspond to A₀ = 0.5. Three different values for the initial rotation parameter are also considered, i.e. S = 1, 1.4, and 2, shown with the blue, pink, and green curves. The left plots refer to the evolution of black hole mass, the middle plot shows the accretion rate temporal behavior, and the panels to the right demonstrate the evolution of the black hole spin parameter. Models are labelled in the middle panels with symbols referring to Table A.1.