  We present measurements of the angular momentum flux (torque) in
Taylor-Couette flow of water between independently rotating cylinders for all
regions of the $\(\Omega_1, \Omega_2\)$ parameter space at high Reynolds
numbers, where $\Omega_1$ $\(\Omega_2\)$ is the inner (outer) cylinder angular
velocity. We find that the Rossby number $Ro = \(\Omega_1 -
\Omega_2\)/\Omega_2$ fully determines the state and torque $G$ as compared to
$G(Ro = \infty) \equiv \Gi$. The ratio $G/\Gi$ is a linear function of
$Ro^{-1}$ in four sections of the parameter space. For flows with
radially-increasing angular momentum, our measured torques greatly exceed those
of previous experiments [Ji \textit{et al.}, Nature, \textbf{444}, 343 (2006)],
but agree with the analysis of Richard and Zahn [Astron. Astrophys.,
\textbf{347}, 734 (1999)].
