observed trimodal MS (Piotto et al. 2007). In case of M13, M3 and M79 there is no apparent ’quantization’ of the MS, and we need to consider the possibility of a continuous distribution of Y along the HB.\
We stress here that in these cases the modeling of the Y variations along the HB becomes more uncertain since calculations require more assumptions. Therefore the main goal of this work is not to attempt an exact description of the Y distribution, that would be affected by our assumptions, but to understand whether helium plays a role in shaping these very different HBs. UV filters are much better suited than optical ones to address this issue.

Our synthetic HB calculations require the specification of at least 4 parameters, plus the cluster age, that we assume to be equal to 12 Gyr (see Section 3). These four parameters are the minimum value of Y (${\rm Y_{min}}$), the range of He abundances (${\rm \Delta Y}$), the mean value of the mass lost along the RGB ${\rm \Delta M}$ – that in first instance (and for simplicity) we assume to be the same for each Y – and the spread around this mean value (${\rm 