Our research addresses the observed evolution of M_BH and L/L_Edd of type 1 radio-quiet AGNs. Measurements of M_BH and L/L_Edd in a sample of sources at z<0.75 using the “Hβ method” (Netzer & Trakkhtenbrot 2007) as well as new measurements of these properties at 0.75<z<2 using the “Mg ii λ2798 method”) show significant evolution of L/L_Edd for any value of M_BH up to z = 2 (see Figure 1). In a dedicated near-IR project we obtained the most reliable sample of M_BH and L/L_Edd estimates for z ~ 2.3 and z ~ 3.4 AGN (Netzer et al. 2007; Shemmer et al. 2004); the distribution of L/L_Edd is very broad (Figure 1) and ~ 1/2 of the sources have L/L_Edd<0.2, implying t_growth>t_universe and hence an earlier epoch of fast growth. Our on-going Gemini–VLT campaign focuses on z ~ 4.8 sources, with the Mg ii line observed in the H-band (Figure 2). The analysis of ~ 1/3 of the spectra uncovers, again, a broad distribution of L/L_Edd, with several sources having L/L_Edd ≫ 1, suggesting an early episode of fast BH growth.