Fraction of structures hosting an SMBH in the centre of their galaxy as a function of the dark-matter halo mass for a set of redshift (coloured lines). The fraction increases with the dark-matter halo mass to reach a value of 1 for haloes more massive than ≃ 4 × 10¹¹ M_⊙. The insert panel shows the fraction of active galaxy nuclei as a function of the dark-matter halo mass. An SMBH is considered to be active if its bolometric luminosity is higher than 5% of its Eddington luminosity.