  Multi-phase fast, massive outflows have been postulated to play a crucial
role in galaxy evolution. The aim of this work is to constrain the nature and
the fraction of outflowing gas in AGNs, as well as the nuclear conditions
possibly at the origin of such phenomena.
  We present a large spectroscopic sample of X-ray detected SDSS AGNs at z
<0.8. X-ray and optical flux ratio diagnostics are used to select the sample.
Physical and kinematic characterisation are derived re-analysing optical (and
X-ray) spectra.
  We derive the incidence of ionised (~40%) and atomic (< 1%) outflows covering
a wide range of AGN bolometric luminosity, from 10^42 to 10^46 erg/s. We also
derive bolometric luminosities and X-ray bolometric corrections to test whether
the presence of outflows is associated with an X-ray loudness, as suggested by
our recent results obtained studying high-z QSOs.
  We study the relations between the outflow velocity inferred from [O III]
kinematic analysis and different AGN power tracers, such as black hole mass
(M_BH), [O III] and X-ray luminosity. We show a well defined positive trend
between outflow velocity and L_X, for the first time over a range of 5 order of
magnitudes. Overall, we find that in the QSO-luminosity regime and at M_BH>10^8
Msun the fraction of AGNs with outflows becomes >50%. Finally, we discuss our
results about X-ray bolometric corrections and outflow incidence in cold and
ionised phases in the context of an evolutionary sequence allowing two distinct
stages for the feedback phase: an initial stage characterized by X-ray/optical
obscured AGNs in which the atomic gas is still present in the ISM and the
outflow processes involve all the gas components, and a later stage associated
with unobscured AGNs, which line of sight has been cleaned and the cold
components have been heated or exhausted.
