  The N to M (M>N) universal quantum broadcasting of mixed states are proposed
for qubits system. The broadcasting of mixed states is universal and optimal in
the sense that the shrinking factor is independent of input state and achieves
the upper bound. The quantum broadcasting of mixed qubits is a generalization
of the universal quantum cloning machine for identical pure input states. A new
pure state decompositions of the identical mixed qubits are obtained.
