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We present results of a computation of NLO QCD corrections to the productionof an off-shell top--antitop pair in association with an off-shell $\text{W}^+$boson in proton--proton collisions. As the calculation is based on the fullmatrix elements for the process $\text{p}\text{p}\to{\text{e}}^+\nu_{\text{e}}\,\mu^-\bar{\nu}_\mu\,\tau^+\nu_\tau\,{\text{b}}\,\bar{\text{b}}$,all off-shell, spin-correlation, and interference effects are included. The NLOQCD corrections are about $20\%$ for the integrated cross-section. Using adynamical scale, the corrections to most distributions are at the same level,while some distributions show much larger $K$-factors in suppressed regions ofphase space. We have performed a second calculation based on a double-poleapproximation. While the corresponding results agree with the full calculationwithin few per cent for integrated cross-sections, the discrepancy can reach$10\%$ and more in regions of phase space that are not dominated bytop--antitop production. As a consequence, on-shell calculations should only betrusted to this level of accuracy.

NLO QCD corrections to off-shell $\text{t}\bar{\text{t}}\text{W}^+$ production at the LHC