Quasar bolometric luminosity functions (L_bol) at z ∼ 0.5, 1.0, 2.0, and 3.0 predicted by L-Galaxies when MS (red) and MSII (black) DM merger trees are used. For comparison, the grey dashed lines represent the luminosity functions of L-Galaxies applied in addition to MSII when a cut of ≥10⁷ M_⊙ in black hole mass is performed. For comparison, these predictions are compared with the data presented in Shen et al. (2020; blue circles). In all the plots, error bars correspond to the Poissonian error (large error bars correspond to the cases where only one object is found).