  Motivated by quantum network applications over classical channels, we
initiate the study of $n$-party resource states from which LOCC protocols can
create EPR-pairs between any $k$ disjoint pairs of parties. We give
constructions of such states where $k$ is not too far from the optimal $n/2$
while the individual parties need to hold only a constant number of qubits. In
the special case when each party holds only one qubit, we describe a family of
$n$-qubit states with $k$ proportional to $\log n$ based on Reed-Muller codes,
as well as small numerically found examples for $k=2$ and $k=3$. We also prove
some lower bounds, for example showing that if $k=n/2$ then the parties must
have at least $\Omega(\log\log n)$ qubits each.
