Context. The evidence of a decrease with increasing luminosity in the fraction f abs of absorbed and Compton-thin among X-rayselected (2−10 keV) AGN is observationally well supported, while that of an increase in f abs with redshift is fairly controversial. In a previous paper, the gravitational effect of the SMBH on the molecular interstellar gas, in the central region of the host galaxy, was shown to predict an anti-correlation between f abs and the black-hole mass M BH . Aims. The most recent findings on the distribution of the Eddington ratio λ = L b /L E as a function of M BH and z are used to convert that relationship into one between f abs and both bolometric (L b ) and X-ray (L X ) luminosities at various values of z. Methods. The findings for λ(M BH , z) are properly treated to ensure completeness in the prediction of f abs above a certain luminosity, at values of z = 0.1, 0.35, 0.7, and ≥1. To verify the consequence of these findings alone, we first adopted a distribution of gas surface density Σ, observed in a sample of local spiral galaxies, irrespective of the galaxy morphological type and z. Results. Assuming the Eddington limit, λ = 1, in the λ(M BH , z) distribution as a "natural" cut-off, the predictions are consistent with the existence of an anti-correlation between f abs and L X , but they fail to reproduce an increase in f abs with z. Because the early type galaxies are on average much poorer in molecular gas than late type ones, a quantitative agreement with the local value of f abs requires the existence of a correlation between Σ and the central activity. An increase in typical values of Σ with z, correlated with the activity, might explain an increase in f abs with z. However, f abs could hardly exceed about 0.3 at the highest luminosities.