If I understand correctly, the escape velocity is $c$ at the event horizon of a black hole. This would seem to mean that an object falling into the black hole from an infinite distance would attain velocity $c$ - regardless of the size of the black hole.
I presume the above reasoning is flawed. For one thing, to an external observer an object slows down due to time dilation and never enters the event horizon at all, never mind at light speed.
What I want to know is, since the Newtonian approach doesn't work, what is the gravitational potential of an infinitely distant object with respect to a black hole, and how does it vary with the black hole's size? Since nothing escapes the event horizon I'm only asking about the energy that can be extracted outside of the horizon.