Black hole mass function (left), bolometric luminosity function (centre), and Eddington ratio distribution (right) at redshift 0, 2 and 4 (top to bottom). The dashed lines show the respective models including an accretion disk model. Despite the very different nature of the accretion models, the resulting mass and luminosity functions are relatively similar. The second set of thinner lines in the Eddington ratio distribution are SMBHs with mass exceeding 10⁷ M_⊙ to be comparable to the literature values of Schulze et al. (2015). Lines with accretion disk models are not shown for clarity.