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We present the resistively-determined upper critical field H^{\rho}{c2}(T) and the irreversibility lines H^{\rho}{irr}(T) of various high-T_c cuprates, deduced from measurements in 61-T pulsed magnetic fields applied parallel to the c-axis. The SHAPE of both H^{\rho}{c2}(T) and H^{\rho}{irr}(T) depends monotonically on the anisotropy of the material and none of the samples show saturation of H^{\rho}(T) at low temperatures. The anomalous positive curvature, d^2 H^{\rho}/dT^2 > 0, is the strongest in materials with the largest normal-state anisotropy, regardless of whether anisotropy is varied by changing the carrier concentration or by comparing a variety of optimally-doped compounds.

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