  Here, asymmetric phase-covariant quantum cloning machines are defined and
trade-off between qualities of their outputs and its impact on entanglement
properties of the outputs are studies. In addition, optimal families among
these cloners are introduced and also their entanglement properties are
investigated. An explicit proof of optimality is presented for the case of
qubits, which is based on the no-signaling condition. Our optimality proof can
also be used to derive an upper bound on trade-off relations for a more general
class of optimal cloners which clone states on a specific orbit of the Bloch
sphere. It is shown that the optimal cloners of the equatorial states, as in
the case of symmetric phase-covariant cloning, give rise to two separable
clones, and in this sense these states are unique. For these cloners it is
shown that total output is of GHZ-type.
