  We consider cloning transformations of equatorial qubits and qutrits, with
the transformation covariant for rotation of the phases. The optimal cloning
maps are derived without simplifying assumptions from first principles, for any
number of input and output qubits, and for a single input qutrit and any number
of output qutrits. We also compare the cloning maps for global and single
particle fidelities, and we show that the two criteria lead to different
optimal maps.
