We study the entanglement dynamics of two cavities interacting with independent reservoirs. Expectedly, as the cavity entanglement is depleted, it is transferred to the reservoir degrees of freedom. We find also that when the cavity entanglement suddenly disappears, the reservoir entanglement suddenly and necessarily appears. Surprisingly, we show that this entanglement sudden birth can manifest before, simultaneously, or even after entanglement sudden death. Finally, we present an explanatory study of other entanglement partitions and of higher dimensional systems.