Implications of a W+W-(ZZ) Higgs boson t(c)over-bar interaction for e+e-→t(c)over-bar-ve(v)over-bare, t(c)over-bar-e+e-, t(c)over-bar-Z and for t→cW+W-, cZZ in a two Higgs doublet model

The standard model with one extra Higgs doublet may give rise to an enhanced tree-level flavor-changing-scalar coupling of a neutral Higgs boson to a pair of top-charm quarks. This coupling map drive a large tree-level effective W+W-(ZZ)-Higgs boson-t (c) over bar interaction. As a result we find that the reactions e(+)e(-) --><t(c)over bar>v(e) (v) over bar(e), t(c) over barZ$ 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)over bar> v(e) (v) over bar(e), <t(c)over 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 root s= 0.5-2 TeV if the mass of the lightest neutral Higgs boson is a few hundred GeV. The rare decays t-->cW(+)W(-) and t-->cZZ may be accessible at the CERN LHC if the mass of the lightest neutral Higgs boson lies in the narrow window 150 GeV less than or similar to m(h) less than or similar to 200 GeV.