Taylor–Couette flow with independently rotating inner (
$i$) and outer (
$o$) cylinders is explored numerically and experimentally to determine the effects of the radius ratio
$\eta $ on the system response. Numerical simulations reach Reynolds numbers of up to
$\mathit{Re}_i=9.5\times 10^3$ and
$\mathit{Re}_o=5\times 10^3$, corresponding to Taylor numbers of up to
$\mathit{Ta}=10^8$ for four different radius ratios
$\eta =r_i/r_o$ between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette (
$\mathrm{T^3C}$) set-up, reach Reynolds numbers of up to
$\mathit{Re}_i=2\times 10^6$ and
$\mathit{Re}_o=1.5\times 10^6$, corresponding to
$\mathit{Ta}=5\times 10^{12}$ for
$\eta =0.714\mbox{--}0.909$. Effective scaling laws for the torque
$J^{\omega }(\mathit{Ta})$ are found, which for sufficiently large driving
$\mathit{Ta}$ are independent of the radius ratio
$\eta $. As previously reported for
$\eta =0.714$, optimum transport at a non-zero Rossby number
$\mathit{Ro}=r_i |\omega _i-\omega _o |/[2(r_o-r_i)\omega _o]$ is found in both experiments and numerics. Here
$\mathit{Ro}_{opt}$ is found to depend on the radius ratio and the driving of the system. At a driving in the range between
$\mathit{Ta}\sim 3\times 10^{8}$ and
$\mathit{Ta}\sim 10^{10}$,
$\mathit{Ro}_{opt}$ saturates to an asymptotic
$\eta $-dependent value. Theoretical predictions for the asymptotic value of
$\mathit{Ro}_{opt}$ are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.