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 $cosgamma to 0$, 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 $cg to tH/A to ttbar c,; ttbar t$ (same-sign top and triple-top), and $cg to bH^+ to btbar b$. We also discuss some related processes such as $cg to thh$, $tZH$ that depend on $cosgamma$ being nonzero, comment briefly on $gg to H/A to tbar t, tbar c$ resonant production, and touch upon the $rho_{tu}$ coupling.
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