Bolometric luminosity function for the actual MBHs in the simulation (“true”) and for the models described in Table 1, where “resc” means we have corrected the number densities for the overdensity bias: OBELISK is a protocluster. To obtain the cosmic average we have rescaled the OBELISK galaxy mass function to that of the NEWHORIZON simulation, which simulates an average region of the Universe. This figure assumes an active fraction of unity, and therefore represents an upper limit to the LF for each of the models. The results are compared to the luminosity functions derived in Matthee et al. (2024, M+24) and Greene et al. (2024, G+24) from JWST data and to fits to the evolution of the bolometric luminosity function derived in Shen et al. (2020, S+20, pre-JWST).