  In the simplest type-I seesaw leptogenesis scenario right-handed neutrino
annihilation processes are absent. However, in the presence of new interactions
these processes are possible and can affect the resulting $B-L$ asymmetry in an
important way. A prominent example is provided by models with spontaneous
lepton number violation, where the existence of new dynamical degrees of
freedom can play a crucial role. In this context, we provide a
model-independent discussion of the effects of right-handed neutrino
annihilations. We show that in the weak washout regime, as long as the
scattering processes remain slow compared with the Hubble expansion rate
throughout the relevant temperature range, the efficiency can be largely
enhanced, reaching in some cases maximal values. Moreover, the $B-L$ asymmetry
yield turns out to be independent upon initial conditions, in contrast to the
"standard" case. On the other hand, when the annihilation processes are fast,
the right-handed neutrino distribution tends to a thermal one down to low
temperatures, implying a drastic suppression of the efficiency which in some
cases can render the $B-L$ generation mechanism inoperative.
