  The correlation between the cosmological rest-frame nuFnu spectrum peak
energy, Ep,i, and the isotropic equivalent radiated energy, Eiso, discovered by
Amati et al. in 2002 and confirmed/extended by subsequent osbervations, is one
of the most intriguing and debated observational evidences in Gamma-Ray Bursts
(GRB) astrophysics. In this paper I provide an update and a re-analysis of the
Ep,i - Eiso correlation basing on an updated sample consisting of 41 long
GRBs/XRFs with firm estimates of z and observed peak energy, Ep,obs, 12 GRBs
with uncertain valeus of z and/or Ep,obs, 2 short GRBs with firm estimates of z
and Ep,obs and the peculiar sub-energetic events GRB980425/SN1998bw and
GRB031203/SN2003lw. In addition to standard correlation analysis and power-law
fitting, the data analysis here reported includes a modelization which accounts
for sample variance. All 53 classical long GRBs and XRFs, including 11 Swift
events with published spectral parameters and fluences, have Ep,i and Eiso
values, or upper/lower limits, consistent with the correlation, which shows a
chance probability as low as ~7x10{-15}, a slope of ~0.57 (~0.5 when fitting by
accounting for sample variance) and an extra-Poissonian logarithmic dispersion
of ~0.15, it extends over ~5 orders of magnitude in Eiso and ~3 orders of
magnitude in Ep,i and holds from the closer to the higher z GRBs. I also
discuss the main implications of the updated Ep,i - Eiso correlation for the
models of the physics and geometry of GRB emission, its use for discriminating
different classes and as a pseudo-z estimator, and the tests of possible
selection effects with GRBs of unknown redshift.
