  For a sample of long GRBs with known redshift, we study the distribution of
the evolutionary tracks on the rest-frame luminosity-peak energy Liso-Ep'
diagram. We are interested in exploring the extension of the `Yonetoku'
correlation to any phase of the prompt light curve, and in verifying how the
high-signal prompt duration time, Tf, in the rest frame correlates with the
residuals of such correlation (Firmani et al. 2006). For our purpose, we
analyse separately two samples of time-resolved spectra corresponding to 32
GRBs with peak fluxes >1.8 phot cm^-2 s^-1 from the Swift-BAT detector, and 7
bright GRBs from the CGRO-BATSE detector previously processed by Kaneko et al.
(2006). After constructing the Liso-Ep' diagram, we discuss the relevance of
selection effects, finding that they could affect significantly the
correlation. However, we find that these effects are much less significant in
the Liso x Tf-Ep' diagram, where the intrinsic scatter reduces significantly.
We apply further corrections for reducing the intrinsic scatter even more. For
the sub-samples of GRBs (7 from Swift and 5 from CGRO) with measured jet break
time, we analyse the effects of correcting Liso by jet collimation. We find
that (i) the scatter around the correlation is reduced, and (ii) this scatter
is dominated by the internal scatter of the individual evolutionary tracks.
These results suggest that the time, integrated `Amati' and `Ghirlanda'
correlations are consequences of the time resolved features, not of selection
effects, and therefore call for a physical origin. We finally remark the
relevance of looking inside the nature of the evolutionary tracks.
