Figure 7: Comparison of empirical estimates of the BHMF (grey shaded region) with BHMFs predicted by theoretical models for SMBH formation and growth (red shaded region), in both the local universe (a) and at (b). Also shown are the estimated BHMFs of broad-line AGN only (solid green line), from Schulze and Wisotzki [121] (a) and Kelly et al. [115] (b). The empirical estimates of the BHMF are those shown in Figures 3 and 4, while the theoretical estimates are those shown in Figure 6. The shaded regions define the spread in the estimates and models and may be considered to be a crude estimate of their uncertainty. In general, the theoretical number densities are consistent with the empirical ones to within a factor of a few.