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The conventional picture of overdoped cuprates as BCS d-wave superconductors has been recently challenged, with the roles of disorder and quantum fluctuations under debate. To address these questions, we focus on the highly overdoped regime, which we have explored via measurements of linear transport and voltage-current characteristics on the hole-doped, La free, Bi_2+xSr_2-xCuO_6+δ (Bi2201) single crystals with zero-resistance transition temperatures T_c ~ 5 K. Measurements were performed in magnetic fields (H) up to 45 T and temperatures (T) down to 17 mK. We discuss the nature of the H-field-tuned superconducting quantum phase transition and the high-field ground state, and present the T-H phase diagram for the highly overdoped Bi2201.