In theories where B - L is a spontaneously broken local symmetry, the
cosmological baryon asymmetry can be generated by the out-of-equilibri
um decay of heavy Majorana neutrinos. We study this mechanism assuming
a similar pattern of mixings and masses for leptons and quarks, as su
ggested by SO(10) unification. This implies that B - L is broken at th
e unification scale Lambda(GUT) similar to 10(16) GeV, if m(nu mu) sim
ilar to 3.10(-3) eV as preferred by the MSW explanation of the solar n
eutrino deficit. The observed value of the baryon asymmetry, n(B)/s si
milar to 10(-10), is then obtained without any fine tuning of paramete
rs.