Three distant labs A, B and C, having no prior entanglement can establish a shared GHZ state, when one of them say A sends two particles to B and C for their local actions. The mediating particles remain separable from each other and from the particles of A, B and C. We prove that in this way, GHZ states are shared with a probability 1/7. We also show how separable particles can be mediated to establish arbitrary d- dimensional Bell states between distant labs. Our method is constructive and

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... ows generaization of GHZ sharing between any number of parties and in any dimension. The proposed method may facilitate the construction of multi-node quantum networks and many other processes which use multi-partite entangled states.