Current in a Brushless DC Motor
$$T_m-J\frac{d²\Theta}{dt²}+F\frac{d\Theta}{dt}-T_L=0$$ 
$$T_m=k_Ti$$
Where \$T_m\$ is motor torque, \$T_L\$ is the load torque, \$J\$ is the moment of inertia, \$F\$ is the friction coefficient, \$\Theta\$ is the rotor angle. \$k_t\$ is torque constant.

There is no max. current vs. speed. It's just a nominal current which may not be exceeded if you look at the current as mean value. The peaks can be very high with respect to the nominal current, but they may not persist for long time - \$I^2t\$ limit.
If we ommit the transients of acceleraton/decelration and friction, then the formula becomes: \$T_m=T_L\$ or \$i=\dfrac{T_L}{k_T}\$