We thoroughly discuss a new supersymmetric grand unified scenario of the triplet seesaw mechanism where the exchange of heavy SU(2)_W triplet states generates both neutrino masses and soft supersymmetry breaking terms. This framework, recently proposed by us in a previous work, is highly predictive since it contains only three free parameters connecting low-energy neutrino parameters, lepton and quark flavour violation, sparticle and Higgs boson spectra and electroweak symmetry breakdown. These three parameters are the triplet mass M_T, the effective supersymmetry breaking scale B_T and a coupling constant lambda. We perform a complete analysis of the parameter space taking into account the present experimental constraints and considering different types of neutrino spectrum. A special emphasis is given to the particular features of the sparticle and Higgs spectra and to the model independent predictions obtained for the processes mu-> e X, mu-> e conversion in nuclei, tau-> e Y and tau-> mu Y (X = gamma, e e, Y= gamma, e e, mu mu). In the appendices, we present some technical aspects relevant for our analysis.

54 LaTeX pages. Typos corrected. Final version to appear in Nucl. Phys. B