  We address the problem of broadcasting N copies of a generic qubit state to
M>N copies by estimating its direction and preparing a suitable output state
according to the outcome of the estimate. This semiclassical broadcasting
protocol is more restrictive than a general one, since it requires an
intermediate step where classical information is extracted and processed.
However, we prove that a suboptimal superbroadcasting, namely broadcasting with
simultaneous purification of the local output states with respect to the input
ones, is possible. We show that in the asymptotic limit of $M \to \infty$ the
purification rate converges to the optimal one, proving the conjecture that
optimal broadcasting and state estimation are asymptotically equivalent. We
also show that it is possible to achieve superbroadcasting with simultaneous
inversion of the Bloch vector direction (universal NOT). We prove that in this
case the semiclassical procedure of state estimation and preparation turns out
to be optimal. We finally analyse semiclassical superbroadcasting in the
phase-covariant case.
