Re: From where does the extreme gravity of a black hole originate?

You are correct.  The gravitational force of an object (star) is inversely 
proportional to the square of the distance from the center of the star to 
another mass (e.g. you).  For a star, all its mass acts as if it were 
concentrated at the center. If you image yourself as being on the outer 
edge of the star, then as the star collapses, the center of the star and 
its outer edge get closer and closer together.  Hence the gravity that the 
outer edge experiences becomes greater and greater. Eventually we believe 
that all the mass of the black hole ends up at the center (called a 
singularity) and if you were at the singularity, then you would experience 
an infinitely large gravitational force. However, as the star collapses, 
there is point where the force of gravity at the outer edge of the star is 
so great that the velocity of escape from the edge is equal to the speed 
of light.  That 
distance from the center is called the event horizon, often referred to as 
the radius of the black hole. For a mass like the sun that would be 3 km.

velocity of escape= square root(2xmass of the Black Hole/distance from the 
center of the black hole)=c (velocity of light)

The reason the sun's gravity is not so large because when you are on the 
edge of the sun, you would be 700,000 km from the center.  As you go into 
the sun, only the mass between you and the center of the sun produces the 
gravity you would feel.  The force of gravity of the mass between you and 
the edge of the sun, cancels out and produces no net force on you.

Reference: Any introductory astronomy text.