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 th
e 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.
