  We investigate the universal asymmetric cloning of states in a Hilbert space
of arbitrary dimension. We derive the class of optimal and fully asymmetric
1->3 cloners, which produce three copies, each having a different fidelity. A
simple parametric expression for the maximum achievable cloning fidelity
triplets is then provided. As a side-product, we also prove the optimality of
the 1->2 asymmetric cloning machines that have been proposed in the literature.
