The high-T-c superconductor Tl2Ba2CuO6+delta is studied by angle-resolved photoemission spectroscopy. For a very overdoped T-c=30 K sample, the Fermi surface consists of a single large hole pocket centered at (pi,pi) and is approaching a topological transition. Although a superconducting gap with d(x)(2)-y(2) symmetry is tentatively identified, the quasiparticle evolution with momentum and binding energy exhibits a marked departure from the behavior observed in under and optimally doped cuprates. The relevance of these findings to scattering, many-body, and quantum-critical phenomena is discussed.