Top panel: a collection of AGN luminosity functions at z ≲ 2 from La Franca et al. (2005), and z > 3 in this work. Central panel: SMBH mass functions obtained by combining the AGN luminosity functions in the top panel with Eddington ratio distributions (see the text for details). Bottom panel: a collection of galaxy stellar mass functions. z ≲ 2 from Fontana et al. (2006), z = 3–4 from Santini et al. (2011), z = 4–5 from Caputi et al. (2011), and z = 6 from Stark et al. (2009).