  We analyze the global transport properties of turbulent Taylor-Couette flow
in the strongly turbulent regime for independently rotating outer and inner
cylinders, reaching Reynolds numbers of the inner and outer cylinders of Re_i =
2 x 10^6 and Re_o = 1.4 x 10^6, respectively. For all Re_i, Re_o, the
dimensionless torque G scales as a function of the Taylor number Ta (which is
proportional to the square of the difference between the angular velocities of
the inner and outer cylinders) with a universal effective scaling law G \propto
Ta^{0.88}, corresponding to Nu_omega \propto Ta^{0.38} for the Nusselt number
characterizing the angular velocity transport between the inner and outer
cylinders. The exponent 0.38 corresponds to the ultimate regime scaling for the
analogous Rayleigh-Benard system. The transport is most efficient for the
counterrotating case along the diagonal in phase space with omega_o \approx
-0.4 omega_i.
