  We describe various results related to the random distillation of multiparty
entangled states - that is, conversion of such states into entangled states
shared between fewer parties, where those parties are not predetermined. In
previous work [Phys. Rev. Lett. 98, 260501 (2007)] we showed that certain
output states (namely Einstein-Podolsky-Rosen (EPR) pairs) could be reliably
acquired from a prescribed initial multipartite state (namely the W state) via
random distillation that could not be reliably created between predetermined
parties. Here we provide a more rigorous definition of what constitutes
``advantageous'' random distillation. We show that random distillation is
always advantageous for W-class three-qubit states (but only sometimes for
Greenberger-Horne-Zeilinger (GHZ)-class states). We show that the general class
of multiparty states known as symmetric Dicke states can be readily converted
to many other states in the class via random distillation. Finally we show that
random distillation is provably not advantageous in the limit of multiple
copies of pure states.
