Mean bolometric luminosity of BH progenitors as a function of the mean BH mass predicted by the reference model (black solid line) and by the model with |$\dot{M}_{\rm accr} \le 20 \, \dot{M}_{\rm Edd}$| (yellow solid line). For each model, the lines show the average among the 29 merger trees and the shaded regions are the 1σ dispersion. The data points show the observational values of the two quasars SDSS J1149 (red circle) and ULAS J1120 (green square). The diagonal dashed lines show some reference values of the luminosity in units of the Eddington luminosity.