  We introduce a repeater scheme to efficiently distribute multipartite
entangled states in a quantum network with optimal scaling. The scheme allows
to generate graph states such as 2D and 3D cluster states of growing size or
GHZ states over arbitrary distances, with a constant overhead per node/channel
that is independent of the distance. The approach is genuine multipartite, and
is based on the measurement-based implementation of multipartite hashing, an
entanglement purification protocol that operates on a large ensemble together
with local merging/connection of elementary building blocks. We analyze the
performance of the scheme in a setting where local or global storage is
limited, and compare it to bipartite and hybrid approaches that are based on
the distribution of entangled pairs. We find that the multipartite approach
offers a storage advantage, which results in higher efficiency and better
performance in certain parameter regimes. We generalize our approach to
arbitrary network topologies and different target graph states.
