  The right--handed neutrino mass matrix that is central to the understanding
of small neutrino masses via the seesaw mechanism can arise either (i) from
renormalizable operators or (ii) from nonrenormalizable or super-renormalizable
operators, depending on the symmetries and the Higgs content of the theory
beyond the Standard Model. In this paper, we study lepton flavor violating
(LFV) effects in the first class of seesaw models wherein the \nu_R Majorana
masses arise from renormalizable Yukawa couplings involving a B-L = 2 Higgs
field. We present detailed predictions for \tau -> \mu + \gamma and \mu -> e +
\gamma branching ratios in these models taking the current neutrino oscillation
data into account. Focusing on minimal supergravity models, we find that for a
large range of MSSM parameters suggested by the relic abundance of neutralino
dark matter and that is consistent with Higgs boson mass and other constraints,
these radiative decays are in the range accessible to planned experiments. We
compare these predictions with lepton flavor violation in the second class of
models arising entirely from the Dirac Yukawa couplings. We study the
dependence of the ratio r \equiv B(\mu -> e+\gamma)/B(\tau ->\mu +\gamma) on
the MSSM parameters and show that measurement of r can provide crucial insight
into the origin of the seesaw mechanism.
