  We study single top quark production in association with a $WZ$ pair at the
LHC in the context of the Standard Model (SM) and the Standard Model Effective
Field Theory (SMEFT). A significant advantage of $tWZ$ compared to other EW top
production processes is its sensitivity to unitarity-violating behaviour
induced in its $2\to2$ sub-amplitudes through modified EW interactions. At NLO
in QCD, $tWZ$ interferes with $t\bar{t}Z$ and $t\bar{t}$ and a method to
meaningfully separate it from these overlapping processes needs to be employed.
In order to define $tWZ$ production for total rates and differential
distributions, we consider the approaches proposed in the literature for
similar cases and find that diagram-removal procedures provide reliable results
both for the SM and the SMEFT in a suitably defined phase-space region. We
provide robust results for total and differential cross sections for $tWZ$ at
13 TeV, including the six relevant dimension-6 operators
($\mathcal{O}_{tW}$,$\mathcal{O}_{tZ}$,$\mathcal{O}_{tG}$,$\mathcal{O}_{\phi
Q}^{(-)}$,$\mathcal{O}_{\phi Q}^{(3)}$,$\mathcal{O}_{\phi t}$), also matching
short-distance events to parton shower.
