  A short summary of results for top-quark pair production in association with
a jet with NLO QCD off-shell effects at the LHC is given. The calculation is
based on the matrix element for the $pp \to e^+ \nu_e \mu^-\bar{\nu}_\mu
b\bar{b} j$ process. All quantum effects are properly accounted for, which
amounts to including all Feynman diagrams that result in this final state with
interference effects as well as non-zero top-quark width effects. Results for
total cross sections and a few differential distributions at the LHC Run1
energy of $\sqrt{s}=8$ TeV are presented. In addition, the size of top-quark
off-shell effects is quantified for the total cross section in presence of
rather inclusive cuts on all final states. Numerical results shown in this
proceedings have been obtained with the HELAC-NLO Monte Carlo program.
