  We explore the evolution with redshift of the rest-frame colours and space
densities of AGN hosts (relative to normal galaxies) to shed light on the
dominant mechanism that triggers accretion onto supermassive black holes as a
function of cosmic time. Data from serendipitous wide-area XMM surveys of the
SDSS footprint (XMM/SDSS, Needles in the Haystack survey) are combined with
Chandra deep observations in the AEGIS, GOODS-North and GOODS-South to compile
uniformly selected samples of moderate luminosity X-ray AGN [L_X(2-10keV) =
1e41-1e44erg/s] at redshifts 0.1, 0.3 and 0.8. It is found that the fraction of
AGN hosted by red versus blue galaxies does not change with redshift. Also, the
X-ray luminosity density associated with either red or blue AGN hosts remains
nearly constant since z=0.8. X-ray AGN represent a roughly fixed fraction of
the space density of galaxies of given optical luminosity at all redshifts
probed by our samples. In contrast the fraction of X-ray AGN among galaxies of
a given stellar mass decreases with decreasing redshift. These findings suggest
that the same process or combination of processes for fueling supermassive
black holes are in operation in the last 5 Gyrs of cosmic time. The data are
consistent with a picture in which the drop of the accretion power during that
period (1dex since z=0.8) is related to the decline of the space density of
available AGN hosts, as a result of the evolution of the specific
star-formation rate of the overall galaxy population. Scenarios which attribute
the evolution of moderate luminosity AGN since z \approx 1 to changes in the
suppermassive black hole accretion mode are not favored by our results.
