  The Standard Model with one extra Higgs doublet may give rise to enhanced
TREE-LEVEL flavor-changing-scalar coupling of a neutral Higgs to a pair of
top-charm quarks. This coupling may drive a large TREE-LEVEL effective
W^+W^-(ZZ) - Higgs - t c-bar interaction. As a result we find that the
reactions e^+e^- -> t c-bar \nu_e \nu_e-bar, t c-bar e^+ e^-, t c-bar Z and the
two rare top decays t -> cW^+W^-, t -> cZZ become very sensitive probes of such
an effective interaction. The most promising ones, e^+e^- -> t c-bar \nu_e
\nu_e-bar, t c-bar e^+ e^-, may yield several hundreds and up to thousands of
such events at the Next Linear Collider with a center of mass energy of
\sqrt{s}=0.5 - 2 TeV if the mass of the lightest neutral Higgs is a few hundred
GeV. The rare decays t -> cW^+W^- and t -> cZZ may be accessible at the LHC if
the mass of the lightest neutral Higgs lies in the narrow window 150 GeV < m_h
< 200 GeV.
