From Mark Elowitz's excellent Web site on exobiology:

http://www.markelowitz.com/exobiology.htm

Galactic Dyson Spheres

"Very advanced (Type-III) civilizations could group a significant number of their Galaxy's stars into a dense region in the core of their Galaxy. The result would be a sphere of aligned orbiting matter just larger than its Schwarzschild radius, with a black hole at the center. Instead of using stellar energy such a civilization could generate energy using the Penrose effect. The total size of the Galactic Dyson sphere would be on the order of several light-months. Smaller Dyson spheres could also be constructed which harvest the energy from very small black holes. These small black holes radiate intense Hawking radiation, losing mass. If an equivalent amount of mass is dumped into the black hole, it will maintain equilibrium, converting matter into energy which could be collected by the Dyson sphere."

Ever wonder about elliptical galaxies like Messier 87? Three trillion stars packed together in a big ball and a huge, energy-spewing black hole in its center.