New computations of s processing in the Thermally Pulsing Asymptotic Giant
Branch (TP-AGB) phases of Low Mass Stars (LMS) at different metallicities a
re presented. The results are compared with the observed abundances of elem
ents heavier than Fe in post-AGB supergiants and in CH stars (both giants a
nd subgiants), which are the result of mass transfer episodes from AGE comp
anions. Our models explain the observed integrated abundances of heavy and
light s elements ('hs' and 'ls', respectively) down to very low metalliciti
es ([Fe/H] = -3), indicating that an intrinsic dispersion in the neutron ca
pture efficiency exists at any epoch. We also succeed in reproducing the de
tailed photospheric composition in s elements in the stars where this is av
ailable.