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 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.