  We investigate the decay of entanglement of generalized N-particle
Greenberger-Horne-Zeilinger (GHZ) states interacting with independent
reservoirs. Scaling laws for the decay of entanglement and for its finite-time
extinction (sudden death) are derived for different types of reservoirs. The
latter is found to increase with the number of particles. However, entanglement
becomes arbitrarily small, and therefore useless as a resource, much before it
completely disappears, around a time which is inversely proportional to the
number of particles. We also show that the decay of multi-particle GHZ states
can generate bound entangled states.
