  In the course of a systematic exploration of the uncertainties associated to
the input micro- and macro-physics in the modeling of the evolution of
intermediate mass stars during their Asymptotic Giant Branch (AGB) phase, we
focus on the role of the nuclear reactions rates and mass loss. We consider
masses 3<M/Msun<6.5 for a metallicity typical for Globular Cluster, Z=0.001,
and compare the results obtained by computing the full nucleosynthesis with hot
bottom burning (HBB), for a network of 30 elements, using either the NACRE or
the Cameron & Fowler (1988) cross-sections. The results differ in particular
with respect to the Na23 nucleosynthesis (which is more efficient in the NACRE
case) and the magnesium isotopes ratios. For both choices, however, the CNO
nucleosynthesis shows that the C+N+O is constant within a factor of two, in our
models employing a very efficient convection treatment. Different mass loss
rates alter the physical conditions for HBB and the length of the AGB phase,
changing indirectly the chemical yields. These computations show that the
predictive power of our AGB models is undermined by these uncertainties. In
particular, it appears at the moment very difficult to strongly accept or
dismiss that these sources play a key-role in the pollution of Globular
Clusters (GCs)
