Hidden top quark with charged-Higgs-boson decay

In top-quark decays, there may be competition between decays mediated by real or virtual $W$ bosons and decays into a charged Higgs boson. We evaluate the branching fractions to delineate the regions where standard top signals would be suppressed for two-Higgs-doublet models. We also show that both the standard semileptonic-decay signals $t\to b{W}^{+}\to \mathrm{bl}\nu$ and unconventional signatures such as $t\to b{H}^{+}\to b\tau \nu$ may be simultaneously suppressed with suitable parameter choices for any top-quark mass; in such circumstances the top quark would be very difficult to detect at hadron colliders.