  We present a protocol for performing state merging when multiple parties
share a single copy of a mixed state, and analyze the entanglement cost in
terms of min- and max-entropies. Our protocol allows for interpolation between
corner points of the rate region without the need for time-sharing, a primitive
which is not available in the one-shot setting. We also compare our protocol to
the more naive strategy of repeatedly applying a single-party merging protocol
one party at a time, by performing a detailed analysis of the rates required to
merge variants of the embezzling states. Finally, we analyze a variation of
multiparty merging, which we call split-transfer, by considering two receivers
and many additional helpers sharing a mixed state. We give a protocol for
performing a split-transfer and apply it to the problem of assisted
entanglement distillation.
