  We provide an analytical investigation of the entanglement dynamics for a
system composed of an arbitrary number of qubits dissipating into a common
environment. Specifically we consider initial states whose evolution remains
confined on low dimensional subspaces of the operators space. We then find for
which pairs of qubits entanglement can be generated and can persist at steady
state. Finally, we determine the stationary distribution of entanglement as
well as its scaling versus the total number of qubits in the system.
