What maintains a black hole's size?

gravity well is what gives the dimensions of a  black hole and  the mass that  it was made with mass.

hawking radiation is a very unusual  quantum effect that happens at the  very edge of the  blackhole 

it does lower the internal mass by giving the blackhole a NEGATIVE mass object 

and giving the  outside of the event horizon a POSITIVE MASS object  

a very large black hole would last for a very long time  without a noticable size reduction 

who would want to get close enough to the event horizon

The collapsar at the centre of a black hole is indeed a singularity, but its mass remains the same and as a result there is an event horizon at a particular radius, depending on the mass, where escape velocity is greater than the speed of light. Hence everything inside that horizon is on its way to becoming part of the collapsar and is never going to emerge, although Hawking radiation means it will gradually lose mass.

No limiter. It may contain the whole Universe.

Nothing maintains the size of matter once it collapses past the neutron star stage. No force can withstand the gravity. It does collapse to a point singularity of zero volume.

When they talk about a black holes size, they mean the radius of its event horizon. The distance from the singularity at which its escape velocity is the speed of light.

A black hole IS a singularity.

You have several very good answers that correctly describe the overall structure of the black hole.

The issue of whether something exists to prevent the black hole from collapsing to a singularity is a complex one. The idea that seems the most straight forward in called the Einstein-Cartan theory which is a modification of general relativity. General relativity doesn’t allow a twisting (torsion) of spacetime so the description of gravitating mass/energy (stress-energy tensor) doesn’t contain torsion components. 

Einstein-Cartan adds torsion components from the quantum spins of densely packed particles. According to Einstein-Cartan, that will generate a kind of repulsive gravity (expands the spacetime metric) which will prevent collapse to a singularity.

Unfortunately, this makes a difficult theory even more difficult to solve. It’s testability is in question since it is indistinguishable from vanilla general relativity for vacuum solutions (black holes weirdly enough are vacuum solutions).  The non-vacuum region - if Einstein-Cartan is correct - is not observable.

The material forming a black hole does, in fact, collapse all the way to a singularity. The region inside its event horizon is the only thing that maintains an extended volume. (Confusion can arise over whether the term "black hole" refers to the singularity only, or also to the region inside the event horizon.)

The mass of the black hole is assumed to be compressed in a singularity of zero dimension (although technically, since the black hole stretch space time to infinity, it would take an infinite amount of time for the mass to actually go anywhere).

What you are calling the black hole is NOT where the mass is, it is the even't horizon of the black hole, that is the BOUNDARY beyond which anything would need to move faster than the speed of light just to remain in orbit.

A black hole formed after a supernova will be so compressed that there would be no particles present in there that can be called electrons or neutrons or whatever anymore. A singularity actually means that no one knows what there is in there. It's sort of obscure. It's a point in space-time where the laws of physics known to us break down! A black hole itself is a singularity. Black holes can even absorb other matter getting into its event horizon, increase its mass to millions and billions of times that of our sun, but nonetheless will always be called a singularity.

Are you asking about the "event horizon" of a black hole? Or the central object at the center?

For the event horizon, that's not a place where there is any matter. It's just the place where gravity reaches a certain strength, at a certain distance from the center. For a 10 solar mass BH, that distance is 29.5 km from the center.

For the central object ... we don't know that there is anything preventing further collapse. Maybe there is, maybe there isn't. If there is something, it would be a very weird new type of thing, involving quantum physics. We have good understanding of physics down to extreme small sizes, much much smaller than an atom. But once things get smaller than about 10^23 times smaller than an atom, we just don't know what happens. (That's a 1 with 23 zeros after it).