  We investigate supersymmetric scenarios in which neutrino masses are
generated by effective d=6 operators in the Kahler potential, rather than by
the standard d=5 superpotential operator. First, we discuss some general
features of such effective operators, also including SUSY-breaking insertions,
and compute the relevant renormalization group equations. Contributions to
neutrino masses arise at low energy both at the tree level and through finite
threshold corrections. In the second part we present simple explicit
realizations in which those Kahler operators arise by integrating out heavy
SU(2)_W triplets, as in the type II seesaw. Distinct scenarios emerge,
depending on the mechanism and the scale of SUSY-breaking mediation. In
particular, we propose an appealing and economical picture in which the heavy
seesaw mediators are also messengers of SUSY breaking. In this case, strong
correlations exist among neutrino parameters, sparticle and Higgs masses, as
well as lepton flavour violating processes. Hence, this scenario can be tested
at high-energy colliders, such as the LHC, and at lower energy experiments that
measure neutrino parameters or search for rare lepton decays.
