  In this paper we study the Flavor-Changing mediated by Higgs boson within
Two-Higgs Doublet Model-III context. We explore the parameter space and,
considering recent results, find new limits for the model parameters. We also
obtain the total Higgs decay width and the branching ratios for different
channels taking limits for the $t\to cV$ and $b\to s\gamma$ processes.
Considering different constraints, we estimate the branching ratio for the
$h\to t^*_{}c$ in the model as well as the bounds for the $b \to s\gamma$, $h
\to \mu\tau$ and $h\to \gamma Z.$ Considering the quark top decays to
$W\bar{b},$ we obtained $Br(h \to Wc\bar{b})\sim10^{-3}$.
