  We present the various leptogenesis scenarios which may occur if, in addition
to the ordinary heavy right-handed neutrinos, there exists a heavy scalar
SU(2)_L triplet coupled to leptons. We show that the contributions of the
right-handed neutrinos and the triplet to the lepton asymmetry are proportional
to their respective contributions to the neutrino mass matrix. A consequence of
the triplet contribution to the lepton asymmetry is that there is no more upper
bound on the neutrino masses from leptogenesis due to the fact that the
neutrino mass constraints do not necessarily induce asymmetry washout effects.
We also show how such a triplet leptogenesis mechanism may emerge naturally in
the framework of the left-right symmetric theories, such as Pati-Salam or
SO(10).
