  In Type III seesaw model, there are tree level flavor changing neutral
currents (FCNC) in the lepton sector, due to mixing of charged particles in the
leptonic triplet introduced to realize seesaw mechanism, with the usual charged
leptons. In this work we study these FCNC effects in a systematic way using
available experimental data. Several FCNC processes have been studied before.
The new processes considered in this work include: lepton flavor violating
processes $\tau \to P l$, $\tau \to V l$, $V \to l \bar l'$, $P \to l \bar l'$,
$M\to M' l \bar l'$ and muonium-antimuonium oscillation. Results obtained are
compared with previous results from $l_i \to l_j l_k \bar l_l$, $l_i \to l_j
\gamma$, $Z \to l \bar l'$ and $\mu - e$ conversion. Our results show that the
most stringent constraint on the $e$-to-$\tau$ FCNC effect comes from $\tau \to
\pi^0 e$ decay. $\tau \to \rho^0 \mu$ and $\tau \to \pi^0 \mu$ give very
stringent constraints on the $\mu$-to-$\tau$ FCNC effect, comparable with that
obtained from $\tau \to \mu \bar \mu \mu$ studied previously. The constraint on
the $e$-to-$\mu$ FCNC effect from processes considered in this work is much
weaker than that obtained from processes studies previously, in particular that
from $\mu - e$ conversion in atomic nuclei. We find that in the canonical
seesaw models the FCNC parameters, due to tiny neutrino masses, are all
predicted to be much smaller than the constraints obtained here, making such
models irrelevant. However, we also find that in certain special circumstances
the tiny neutrino masses do not directly constrain the FCNC parameters. In
these situations, the constraints from the FCNC studies can still play
important roles.
