No, black holes never get full. The size of a black hole is fixed by the amount of mass it contains. For each increment of mass the size of the Sun, its radius grows by 1.7 miles, so if a black hole has a mass of 10 times the Sun, its radius is 17 miles. The more matter that falls into it, the bigger it gets, so in fact it never fills up inside. If a black hole consumes matter at too ferocious a rate, the radiation pressure generated by the infalling matter provides tremendous resistance to the flow of matter. The rate at which matter can fall into a black hole is regulated to what is called the Eddington Accretion Rate. For a solar-mass black hole, this rate equals the mass of our Sun consumed every 100 million years.
