that it is not possible to reproduce the complex HB zoology with a single [“global”]{} parameter, but more likely we can explain it by thinking of a [“global combination”]{} of [“non-global”]{} quantities and phenomena related to the formation, chemical and dynamical evolution of each cluster.\
The necessity of at least a third parameter transpires also from D10 and G10 analyses, in the form of either the luminosity cluster density or stellar density ($\log(\rho)$) – as already suggested by Fusi Pecci et al. (1993) – which might correlate with the hot extension of the HBs, or a variation of the initial helium abundance (Y), respectively.\
Indeed D’Antona et al. (2005) and Dalessandro et al. (2011 – hereafter PaperI) have shown that for NGC2808 the main parameter that determines the HB morphology is Y. In particular in PaperI we have been able to satisfactory reproduce the cluster complex HB morphology by assuming three different sub-populations with He abundances compatible with what inferred from the multimodal Main Sequence (MS; Piotto et al. 2007) and spectroscopic analyses (Bragaglia et al. 2010; Pasquini et al. 2011). It is worth noticing however that only few clusters show evidences of multiple sub-populations with different He abundances as 