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Abstract. Several experimental and theoretical studies indicate the existence of a critical point separating the underdoped and overdoped regions of the high-T c cuprates' phase diagram. There are at least two distinct proposals on the critical concentration and its physical origin. First one is associated with the pseudogap formation for p < p * , with p * ≈ 0.2. Another one relies on the Hall effect measurements and suggests that the critical point and the quantum phase transition (QPT) take place at optimal doping, p opt ≈ 0.16. Here we have performed a precise density of states calculation and found that there are two QPTs and the corresponding critical concentrations associated with the change of the Fermi surface topology upon doping.