  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 $\frac{1}{7}$. We also show how separable particles
can be mediated to establish arbitrary $d-$ dimensional Bell states between
distant labs. Our method is constructive and allows 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.
