  Long-lived stars in GCs exhibit chemical peculiarities with respect to their
halo counterparts. In particular, Na-enriched stars are identified as belonging
to a 2d stellar population born from cluster material contaminated by the
H-burning ashes of a 1st stellar population. Their presence and numbers in
different locations of the CMDs provide important constraints on the
self-enrichment scenarios. In particular, the ratio of Na-poor to Na-rich stars
on the AGB has recently been found to vary strongly from cluster to cluster,
while it is relatively constant on the RGB. We investigate the impact of both
age and metallicity on the theoretical Na spread along the AGB within the
framework of the fast rotating massive stars scenario for GC self-enrichment.
(tb continued)
