We report a detailed quantum oscillation study of the overdoped cuprate Tl 2 Ba 2 CuO 6+δ at two different doping levels (T c = 10 and 26 K). The derived Fermi surface size and topology complement earlier angle-dependent magnetoresistance studies and confirm the existence of a large quasi-cylindrical hole-doped Fermi surface with a small, but finite, c-axis warping. An accurate determination of the hole concentration reveals that superconductivity in Tl 2 Ba 2 CuO 6+δ does not follow the universal T c ( p) parabola for cuprate families and survives up to a larger doping of p c = 0.31. The observation of quantum oscillations for both dopings demonstrates that Fermi liquid behaviour is not confined to the edge of the superconducting dome, but is robust up to at least 0.3T max c . Moreover, the observation of such well-resolved oscillations implies that the physical properties of overdoped Tl 2 Ba 2 CuO 6+δ are determined by a single, spatially homogeneous electronic ground state. Finally, analysis of the different quasiparticle masses points towards a purely magnetic or electronic pairing mechanism.