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We study a version of Two Higgs Doublet Models with non-standard flavorviolation in the up quark sector. We find branching ratios for the rare topdecays $t\to hc$ and $t\to hu$ that are within reach of current and futurecolliders, while other flavor constraints from rare $B$ decays and neutral $D$meson mixing, as well as constraints from Higgs signal strength measurementsremain under control. The most prominent collider signature of the consideredsetup is $pp \to t H \to tt \bar c$, providing continued motivation to searchfor same-sign tops at the LHC as well as a simple framework to interpret thesesearches. As a byproduct of our study, we provide updated SM predictions forthe rare top decays BR$(t \to h c)_\text{SM} = (4.19^{+1.08}_{-0.80} \pm 0.16)\times 10^{-15}$ and BR$(t \to h u)_\text{SM} = (3.66^{+0.94}_{-0.70} \pm 0.67)\times 10^{-17}$ with the main uncertainties coming from higher order QCD andCKM matrix elements.

Rare Top Decays as Probes of Flavorful Higgs Bosons