  We study the dynamics of the entanglement structure of a multipartite system
experiencing a dissipative evolution. We characterize the processes leading to
a particular form of output system entanglement and provide a recipe for their
identification via concatenations of particular linear maps with
entanglement-breaking operations. We illustrate the applicability of our
approach by considering local and global depolarizing noises acting on general
multiqubit states. A difference in the typical entanglement behavior of systems
subjected to these noises is observed: the originally genuine entanglement
dissociates by splitting off particles one by one in the case of local noise,
whereas intermediate stages of entanglement clustering are present in the case
of global noise. We also analyze the definitive phase of evolution when the
annihilation of the entanglement compound finally takes place.
