Redshift for galaxies exceeds c because the universe is accelerating so fast for us that galaxies must be already moving away at faster than the speed of light.

However redshift as something is thrown into a black hole shouldn't do that, right? Nothing exceeds the speed of light down to the event horizon thus redshift will never exceed c...or could it be that because the infalling object is always in a gravitational field that the redshift will exceed c and go all the way to infinity?