© 2019, The Author(s). Limits are set on the pair production of scalar leptoquarks, where all possible decays of the leptoquark into a quark (t, b) and a lepton (τ, ν) of the third generation are considered. The limits are presented as a function of the leptoquark mass and the branching ratio into charged leptons for up-type (LQ3u → tν/bτ) and down-type (LQ3d → bν/tτ) leptoquarks. Many results are reinterpretations of previously published ATLAS searches. In all cases, LHC proton-proton collision data at a centre-of-mass energy of s = 13 TeV recorded by the ATLAS detector in 2015 and 2016 are used, corresponding to an integrated luminosity of 36.1 fb−1. Masses below 800 GeV are excluded for both LQ3u and LQ3d independently of the branching ratio, with masses below about 1 TeV being excluded for the limiting cases of branching ratios equal to zero or unity.[Figure not available: see fulltext.].