  We present a technique for the dissipative preparation of highly entangled
multiparticle states of atoms coupled to common oscillator modes. By combining
local spontaneous emission with coherent couplings we engineer many-body
dissipation that drives the system from an arbitrary initial state into a
Greenberger-Horne-Zeilinger state. We demonstrate that using our technique,
highly entangled steady states can be prepared efficiently in a time that
scales polynomially with the system size. Our protocol assumes generic
couplings and will thus enable the dissipative production of multiparticle
entanglement in a wide range of physical systems. As an example, we demonstrate
the feasibility of our scheme in state-of-the-art trapped-ion systems.
