The evidence of a decrease with increasing luminosity in the fraction
of Compton-thin AGN (f_abs) is observationally well supported, while
that of an increase of this fraction with redshift is rather
controversial.  
In the frame of observationally based evidence that in Compton-thin
sources the absorbing gas might be located far away from the X-ray
source, we show that the gravitational effect of the black hole on the
molecular interstellar gas, in the central region of the host galaxy,
leads to the prediction of an anti-correlation between f_abs and the
black hole mass (M_BH).
The most recent findings on the distribution of the Eddington ratio as
a function of M_BH and z are used to convert that prediction into one
between f_abs and the luminosity at various values of z.