  We find that the asymptotic entanglement of assistance of a general bipartite
mixed state is equal to the smaller of its two local entropies. Our protocol
gives rise to the asymptotically optimal EPR pair distillation procedure for a
given tripartite pure state, and we show that it actually yields EPR and GHZ
states; in fact, under a restricted class of protocols, which we call "one-way
broadcasting", the GHZ-rate is shown to be optimal.
  This result implies a capacity theorem for quantum channels where the
environment helps transmission by broadcasting the outcome of an optimally
chosen measurement. We discuss generalisations to m parties, and show (for m=4)
that the maximal amount of entanglement that can be localised between two
parties is given by the smallest entropy of a group of parties of which the one
party is a member, but not the other. This gives an explicit expression for the
asymptotic localisable entanglement, and shows that any nontrivial ground state
of a spin system can be used as a perfect quantum repeater if many copies are
available in parallel.
  Finally, we provide evidence that any unital channel is asymptotically
equivalent to a mixture of unitaries, and any general channel to a mixture of
partial isometries.
