  In the so called two Higgs doublet model for the top-quark (T2HDM), first
suggested by Das and Kao, the top quark receives a special status, which endows
it with a naturally large mass, and also potentially gives rise to large flavor
changing neutral currents (FCNC) only in the up-quark sector. In this paper we
calculate the branching ratio (BR) for the rare decays t->ch and h->tc (h is a
neutral Higgs) in the T2HDM, at tree level and at 1-loop when it exceeds the
tree-level. We compare our results to predictions from other versions of 2HDM's
and find that the scalar FCNC in the T2HDM can play a significant role in these
decays. In particular, the 1-loop mediated decays can be significantly enhanced
in the T2HDM compared to the 2HDM of types I and II, in some instances reaching
BR~10^-4 which is within the detectable level at the LHC.
