  We propose a scheme for the generation of entangled states for two atoms
trapped in separate cavities coupled to each other. The scheme is based on the
competition between the unitary dynamics induced by the classical fields and
the collective decays induced by the dissipation of two delocalized field
modes. Under certain conditions, the symmetric or asymmetric entangled state is
produced in the steady state. The analytical result shows that the distributed
steady entanglement can be achieved with high fidelity independent of the
initial state, and is robust against parameter fluctuations. We also find out
that the linear scaling of $F$ has a quadratic improvement compared to
distributed entangled state preparation protocols based on unitary dynamics.
