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Received Hc2-n1.tex)We present the resistively-determined upper critical field H ρ c2 (T ) and the irreversibility lines H ρ irr (T ) of various high-Tc cuprates, deduced from measurements in 61-T pulsed magnetic fields applied parallel to the c axis. The shape of both H ρ c2 (T ) and H ρ irr (T ) depends monotonically on the anisotropy of the material and none of the samples show saturation of H ρ (T ) at low temperatures. The anomalous positive curvature, d 2 H ρ /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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