  Accretion models predict that fluorescence lines broadened by relativistic
effects should arise from reflection of X-ray emission onto the inner region of
the accretion disc surrounding the central black hole of active galactic nuclei
(AGN). The theory behind the origin of relativistic lines is well established,
and observational evidence from a moderate number of sources seems to support
the existence of these lines. The aim of this work is to establish the fraction
of AGN with relativistic Fe Kalpha lines, and study possible correlations with
source physical properties. An XMM-Newton collection of 149 radio-quiet Type 1
AGN has been systematically and uniformly analyzed in order to search for
significant evidence of a relativistically broadened Fe Kalpha line. To enable
statistical studies, an almost complete, flux-limited subsample of 31 sources
has been defined. The 2-10 keV spectra of the FERO sources have been compared
with a complex model including most of the physical components observed in the
X-ray spectra of Seyfert galaxies: a power law primary continuum modified by
non-relativistic Compton reflection and warm absorption, plus a series of
narrow Fe line reflection features. The observed fraction of sources in the
flux-limited sample that show significant evidence of a relativistic Fe Kalpha
line is 36%. The average line Equivalent Width (EW) is of the order of 100 eV,
while the average disc inclination angle is 28+/-5 deg and the average
power-law index of the radial disc emissivity law is 2.4+/-0.4. The spin value
is well constrained only in 2 cases (MCG-6-30-15 and MRK509), and in the rest
of the cases, whenever a constraint can be placed, it always implies the
rejection of the static black hole solution. The Fe Kalpha line EW does not
correlate with disc parameters or with system physical properties, such as
black hole mass, accretion rate and hard X-ray luminosity.
