  We consider qubit networks where adjacent qubits besides interacting via
XY-coupling, also dissipate into the same environment. The steady states are
computed exactly for all network sizes and topologies, showing that they are
always symmetric under permutation of network sites, leading to a uniform
distribution of the stationary entanglement across the network. The maximum
entanglement between two arbitrary qubits is shown to depend only on the total
number of qubits in the network, and scales linearly with it. A possible
physical realization by means of an array of doped cavities is discussed for
the case of a linear chain.
