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 MT, the effective supersymmetry breaking scale BT and a coupling constant λ. 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 μ→eX, μ→e conversion in nuclei, τ→eY and τ→μY (X=γ,ee, Y=γ,ee,μμ). In the appendices, we present some technical aspects relevant for our analysis.