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From a comprehensive statistical analysis of $Swift$ X-ray light-curves ofgamma-ray bursts (GRBs) collected from December 2004 to the end of 2010, wefound a three-parameter correlation between the isotropic energy emitted in therest frame 1-10$^4$ keV energy band during the prompt emission(E$_{\rm{\gamma,iso}}$), the rest frame peak of the prompt emission energyspectrum (E$_{\rm{pk}}$), and the X-ray energy emitted in the rest frame 0.3-30keV observed energy band (E$_{\rm{X,iso}}$), computed excluding thecontribution of the flares. In this paper, we update this correlation with thedata collected until June 2014, expanding the sample size with $\sim$35% moreobjects, where the number of short GRBs doubled. With this larger sample weconfirm the existence of a universal correlation that connects the prompt andafterglow properties of long and short GRBs. We show that this correlation doesnot depend on the X-ray light-curve morphology and that further analysis isnecessary to firmly exclude possible biases derived by redshift measurements.In addition we discuss about the behavior of the peculiar objects as ultra-longGRBs and we propose the existence of an intermediate group between long andshort GRBs. Interestingly, two GRBs with uncertain classification fall intothis category. Finally, we discuss the physics underlying this correlation, inthe contest of the efficiency of conversion of the prompt $\gamma$-ray emissionenergy into the kinetic energy of the afterglow, the photosferic model, and thecannonball model.

Update on the GRB universal scaling E$_{\rm{X,iso}}$-E$_{\rm{\gamma,iso}}$-E$_{\rm{pk}}$ with ten years of $Swift$ data