Massive black hole mass function (top) and median spin for X-ray bright MBHs (bottom) as a function of the MBH mass M_• predicted by the L-Galaxies BH model used in this work. Data are shown for z = 0 (red solid line) and z = 5.5 (yellow dashed line), with shaded areas in the bottom panel referring to the 1σ dispersion at a given mass range. In the top panel, the gray dashed line corresponds to the MBH mass function value equal to 1 dex⁻¹ per MSII simulation volume. The results are compared with observational data at z = 0; MH08, Vika09, Sh09, Cao10, Sh13, Arvs15, GS19, and MuPa16 refer to the model-dependent constraints on the MBH mass function derived respectively by Merloni & Heinz (2008), Cao (2010), Gallo & Sesana (2019), Shankar et al. (2009, 2013), Mutlu-Pakdil et al. (2016), Vika et al. (2009), Aversa et al. (2015). For spin constraints, we display the upper and lower limits from X-ray reflection spectroscopy (Reynolds 2021). For a closer comparison to observational results, the average spin values shown here are for MBHs with a predicted hard X-ray luminosity of log L_HX > 40 erg s⁻¹.