Q:

My question is what happens when two black holes with the same mass, size and everything encounter each other? Question two, what is a quasar?

A:

When two black holes encounter each other, they could form another even more massive black hole. Multiple black holes merging together is one idea scientists have proposed to explain how mid-mass and supermassive black holes might be created. That is, one way really massive black holes might be formed is by two or more stellar black holes encountering each other.

You can read more about these big black holes at:
http://chandra.harvard.edu/xray_sources/bh_midmass.html
http://chandra.harvard.edu/xray_sources/blackholes_sm.html

Quasars are galaxies with supermassive black holes at their centers. Large amounts of material are falling onto a quasar's supermassive black hole, which generates lots of energy (light) that telescopes like Chandra can then observe. Many galaxies are thought to contain supermassive black holes at their centers (including our own galaxy, the Milky Way). But in quasar galaxies, in addition to the supermassive black hole, there is also a lot of material available for the black hole to consume -- and so there's more energy produced.

Matter is consumed by a black hole when the gravitational force of the black hole pulls it beyond the event horizon, from which the matter cannot escape because the gravity is too strong. The ultimate fate of the matter is unknown since nothing, not even light, can escape from inside the event horizon and give us information about what happened to the material. The theory indicates that it must be crushed to an extremely high density -- to a point at which the theory no longer applies! However, since nothing can escape from a black hole, all energy and mass of the matter is captured inside of the black hole. According to the theory, this energy and mass is not destroyed, though it may change forms.