Eddington ratio vs. bolometric luminosity (left panels) and black hole mass (right panels). The simulated AGN sample was divided in two redshift bins, z < 1.2 (top panels) and 1.2 < z < 2.3 (bottom panels), and in unobscured (type-1, N_H < 10²² cm⁻²) and obscured (type-2, 10²² cm⁻² > N_H > 10²² cm⁻²) sources, to match the L12 samples (circles and squares, mean values with 1σ errors). X-ray luminosity lower-limits (as marked on the plots) were also imposed for the same reason. When the lower-luminosity limits are relaxed the results are shown with dotted (type-1) and dashed lines (type-2). Obscuration does not affect the results plotted on the left, therefore only one line is drawn for the two samples. The gray lines are the respective results of the type-1 sample at the high-z range, plotted to demonstrate the evolution. We also plot the results of the AGN8.5 model (dash-dotted lines) and the mean λ values (not corrected for incompleteness) of previous studies at the mean luminosities of their samples. See Sect. 4.2 for more discussion on the observed trends.