  We discuss the effect of the neutrino mass scale on baryogenesis via the
out-of-equilibrium decay of the lightest right-handed (s)neutrinos in type II
see-saw models. We calculate the type II contributions to the decay asymmetries
for minimal scenarios based on the Standard Model and on the Minimal
Supersymmetric Standard Model, where the additional direct mass term for the
neutrinos arises from a Higgs triplet vacuum expectation value. The result in
the supersymmetric case is new and we correct the previous result in the
scenario based on the Standard Model. We confirm and generalize our results by
calculating the decay asymmetries in an effective approach, which is
independent of the realization of the type II contribution. We derive a general
upper bound on the decay asymmetry in type II see-saw models and find that it
increases with the neutrino mass scale, in sharp contrast to the type I case
which leads to an upper bound of about 0.1 eV on the neutrino mass scale. We
find a lower bound on the mass of the lightest right-handed neutrino,
significantly below the corresponding type I bound for partially degenerate
neutrinos. This lower bound decreases with increasing neutrino mass scale,
making leptogenesis more consistent with the gravitino constraints in
supersymmetric models.
