  We consider optimal cloning of the spin coherent states in Hilbert spaces of
different dimensionality d. We give explicit form of optimal cloning
transformation for spin coherent states in the three-dimensional space,
analytical results for the fidelity of the optimal cloning in d=3 and d=4 as
well as numerical results for higher dimensions. In the low-dimensional case we
construct the corresponding completely positive maps and exhibit their
structure with the help of Jamiolkowski isomorphism. This allows us to
formulate some conjectures about the form of optimal coherent cloning CP maps
in arbitrary dimension.
