Distribution of luminosities at rest-frame 2500 Å as a function of redshift for the main (grey points) and the selected (cleaned) samples (see Sect. 7.4). Brown and yellow squares: high-z sample (Salvestrini et al. 2019; Vito et al. 2019, see Sect. 2.6), cyan points: SDSS–4XMM (Sect. 2.1), brown triangles: XMM–XXL (Menzel et al. 2016, Sect. 2.3), orange pentagons: the local AGN sample (Sect. 2.7), red stars: z ≃ 3 quasar sample (Nardini et al. 2019, green star: new z ≃ 4 quasar (Sect. 2.5), gold pentagons: SDSS–Chandra (Sect. 2.2).