We will present the state-of-the-art full off-shell NLO QCD results for the process. The multi-lepton top-quark decay channel at the LHC with TeV will be analysed. In our calculation off-shell top quarks and gauge bosons are described by Breit-Wigner propagators. Furthermore, double-, single- as well as non-resonant top-quark contributions along with all interference effects are consistently incorporated already at the matrix element level. We will present the results at the integrated and differential cross-section level for various renormalisation and factorisation scale settings as well as different PDF sets. Lastly, we will investigate the effects of the additional jet activity in the process by comparing the normalised differential cross-section distributions for and .