  We propose a scheme to probabilistically generate Greenberger-Horne-Zeilinger
(GHZ) states encoded on the path degree of freedom of three photons. These
photons are totally independent from each other, having no direct interaction
during the whole evolution of the protocol, which remarkably requires only
linear optical devices to work, and two extra ancillary photons to mediate the
correlation. The efficacy of the method, which has potential application in
distribited quantum computation and multiparty quantum communication, is
analyzed in comparison with similar proposals reported in the recent
literature. We also discuss the main error sources that limit the efficiency of
the protocol in a real experiment and some interesting aspects about the
mediator photons in connection with the concept of spatial nonlocality.
