Precision studies of the properties of the top quark represent a cornerstone of the LHC physics program. In this contribution we focus on the production of $tbar{t}$ pairs in association with one hard jet and in particular on its connection with precision measurements of the top quark mass at the LHC. We report a summary of a full calculation of the process $pp to e^+ u_emu^-bar{ u}_mu b bar{b}j$ at NLO QCD accuracy, which describes $tbar{t}j$ production with leptonic decays beyond the Narrow Width Approximation (NWA), and discuss the impact of the off-shell effects through comparisons with NWA. Finally we explore the sensitivity of $tbar{t}j$ in the context of top-quark mass extraction with the template method, considering two benchmark observables as case studies.
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