  The $h(125)$ boson, discovered only in 2012, is lower than the top quark in
mass, hence $t \to ch$ search commenced immediately thereafter, with current
limits at the per mille level and improving. As the $t \to ch$ rate vanishes
with the $h$-$H$ mixing angle $\cos\gamma \to 0$, we briefly review the
collider probes of the top changing $tcH/tcA$ coupling $\rho_{tc}$ of the
exotic $CP$-even/odd Higgs bosons $H/A$. Together with an extra top conserving
$ttH/ttA$ coupling $\rho_{tt}$, one has an enhanced $cbH^+$ coupling alongside
the familiar $tbH^+$ coupling, where $H^+$ is the charged Higgs boson. The main
processes we advocate are $cg \to tH/A \to tt\bar c,\; tt\bar t$ (same-sign top
and triple-top), and $cg \to bH^+ \to bt\bar b$. We also discuss some related
processes such as $cg \to thh$, $tZH$ that depend on $\cos\gamma$ being
nonzero, comment briefly on $gg \to H/A \to t\bar t, t\bar c$ resonant
production, and touch upon the $\rho_{tu}$ coupling.
