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We consider a supersymmetric SO(10) model with a SU(3) symmetry of flavour inwhich fermion masses emerge via the see-saw mixing with superheavy fermions in16+16bar representations. In this model the dangerous D=5 operators of protondecay are naturally suppressed and flavour-changing supersymmetric effects areunder control. The mass matrices for all fermion types (up and down quarks,charged leptons as well as neutrinos) appear in the form of combinations ofthree rank-1 matrices, common to all types of fermions, with differentcoefficients that are successive powers of small parameters, related to eachother by SO(10) symmetry properties. Two versions of the model are considered,in which approximate grand unification of masses takes place between quarks andleptons of the first family (with very small \tan\beta) or for the ones of thesecond family (predicting moderate \tan\beta ~ 7-8). The second versionexhibits an interesting mechanism of unification of the determinants of theYukawa matrices of all types of fermions at the GUT scale and it provides aperfect fit of the known data for fermion masses, mixing and CP-violation. Itpredicts a hierarchical pattern of neutrino masses with non-zero theta_e3,within 2-7 degrees. In addition, it predicts the correct sign of the baryonasymmetry of the Universe via the leptogenesys scenario.Comment: 30 Pages, 3 figures. Clarified comments on neutrino scales and on  universal seesaw, updated references. Version appeared on JHE

Supersymmetric SO(10) for fermion masses and mixings: rank-1 structures of flavour