  The production of a single top quark in association with a $\mathrm{Z}$ boson
($\mathrm{t}\mathrm{Z}\mathrm{j}$ production) at the LHC is a relevant probe of
the electroweak sector of the Standard Model as well as a window to possible
new-physics effects. The growing experimental interest in performing
differential measurements for this process demands an improved theoretical
modelling in realistic fiducial regions. In this article we present an
NLO-accurate $\mathrm{t}\mathrm{Z}\mathrm{j}$ calculation that includes
complete off-shell effects and spin correlations, combining QCD and electroweak
radiative corrections to the LO signal. Integrated and differential
cross-sections are shown for a fiducial setup characterized by three charged
leptons, two jets, and missing energy.
