  In theories where $B-L$ is a spontaneously broken local symmetry, the
cosmological baryon asymmetry can be generated by the out-of-equilibrium decay
of heavy Majorana neutrinos. We study this mechanism assuming a similar pattern
of mixings and masses for leptons and quarks, as suggested by SO(10)
unification. This implies that $B-L$ is broken at the unification scale
$\Lambda_{\mbox{\scriptsize GUT}}\sim 10^{16}$ GeV, if $m_{\n_\m} \sim 3\cdot
10^{-3}$eV as preferred by the MSW explanation of the solar neutrino deficit.
The observed value of the baryon asymmetry, $n_B/s \sim 10^{-10}$, is then
obtained without any fine tuning of parameters.
