  We consider the distribution of entanglement from a multi-mode optical
driving source to a network of remote and independent optomechanical systems.
By focusing on the tripartite case, we analyse the effects that the features of
the optical input states have on the degree and sharing-structure of the
distributed, fully mechanical, entanglement. This study, which is conducted
looking at the mechanical steady-state, highlights the structure of the
entanglement distributed among the nodes and determines the relative efficiency
between bipartite and tripartite entanglement transfer. We discuss a few open
points, some of which directed towards the bypassing of such limitations.
