Constraints on the maximum mass that could be observed in a broad-line quasar as a function of redshift. Symbols are as in Figure 5. The maximum value of M _BH for quasars implied by our BHMF is M ^max _BH ~ 4 × 10 ¹⁰  M _☉, although values of 10 ¹⁰ < M ^max _BH/ M _☉ < 10 ¹¹ are consistent within the uncertainties. However, as discussed in the text the values of M ^max _BH we derive are highly sensitive to our adopted prior constraints, and the values shown should be treated as lower limits.