Uncertainty on the predicted MF for SMBHs (blue shaded areas) and for AGN (cyan shaded areas) at different redshifts. This is obtained by combining the results and the related uncertainties from the models with ϵ = 0.05, 0.07, and 0.1. Dotted lines are the lower limits for the BHMF. We note the strong constraints imposed by the models on the evolution of AGN, compared to the large uncertainty in the BHMF at high redshifts.