Gravity is gravity. Gravitational strength can be elegantly summarized by the amount that it redshifts light, which is equivalent to the energy it subtracts from a photon escaping (N.B. that's exactly what "redshift" means), which is equivalent to the escape velocity needed to escape to infinity. (For everyday matter that moves slower than c, we must multiply the energy-per-unit-mass by the mass, which is awkward -- so we divide out the mass, which leaves an acceleration. That's why 1G means 10 m/s^2, in Newtonian units. Ultimately, all of these representations of gravity boil down to the same thing: it's a down, against which energy / velocity / acceleration push upward.)
WLOG, imagine a point mass source, with no radius of its own. Escape velocity at a certain radius is proportional to the mass, and inversely(-square?) proportional to distance from the center. GR's beautiful equations showed the sensational (at that time) result that escape velocity has no limit. Add more mass, and the escape velocity can reach c. Add even more mass, and escape velocity can exceed c. Nothing funky happens to the point mass when the escape velocity hits c. There is (apparently) no law of the universe that caps the velocity-needed-to-escape.
But we also have the theory of SR (special relativity), which states that "nothing can move faster than c", i.e. there is a law of the universe that caps the velocity-you-can-attain. Satisfy both of those theories at the same time, and -- every kind of beautiful funkiness emerges. To satisfy both theories simultaneously, you simply plug-and-chug to find the (finite) radius at which the escape velocity is exactly c, and then ... that's the Schwarzschild radius of the GR solution. Nowadays, we call it the "event horizon" of a "black hole" (although both buzzwords are much more modern than the original GR papers).
With a bit of gedanken-checking (gedanken = thought), you can easily see how this makes sense: a photon moving at c, orbiting exactly at the event horizon, will exactly stay in orbit forever, and neither fall in nor get out. Such an orbit arises whenever a photon exactly skims the event horizon on a tangent vector, and neither misses wide, nor intersects it like a soda straw pushed through a potato. (We think today that every black hole is absolutely buried under mattresses of such trapped photons, comprising a photon shell -- but you'll never see them, because (boomp-chh!) none of them will ever come out to your retina. If you pass through the event horizon, you might get blasted by a photon wall going sideways to you, and maybe reflect some of them inward with you.)
Ergo, a photon 1 femtometer farther away will slowly spiral out (and redshift to almost nothing), because it's faster than the escape velocity thereat. Those slightly inside must slowly spiral inward. Photons moving radially away from the center suffer the same fate: from just-outside the event horizon, they'll escape, but leave most of their energy behind, which for a photon means they become deeeeeep-infrared. Photons from inside the event horizon, moving radially outward, lose all of their energy before they make it out, and so ... they attenuate down to 0 quanta of energy, at which point they kind of just wink out of existence and cease to ripple the electromagnetic field. So photons inside don't make it out, and nothing else does, either.
There's actually nothing special about a "black hole" that gives it anything like "supergravity". GR actually says that mass causes curvature, and curvature deflects motion (and absorbs energy -- or by absorbing energy, haha). Newtonian gravitation is a very elegant approximation of the motions you get when masses move in curved space -- so they're both correct, but GR is "more" correct because it can usefully describe what happens under extreme conditions such as two black holes spiraling around each other. Anyways, curvature (of spacetime) is all the same; it makes no difference what shape the mass is in. Put a huge curtain around the galactic center, so that it hides whatever's inside. The center could be a diffuse cloud of cold dark gas of 4.3 million solar masses, or 4.3 million hot suns of 1 solar mass each, or 7000 dead neutron stars of the same total mass, or 1 black hole of that mass, or whatever else. It matters not; all will create (seen from far enough away) identical curvature in spacetime, and therefore everything around it will orbit that curvature without even noticing any difference. If they would fall into a black hole, they would have fallen into the cold dark gas cloud along exactly the same path. Nothing about "black hole" makes it any more attractive than any other arrangement of the same total mass.
Hence, most galaxies don't fall into their galactic centers. Think about it: for 10 billion years they've been in orbit around something . If they were falling in, they'd have already reached the bottom long ago. So whatever hasn't already fallen, probably won't for at least another 10-20 billion years. Orbits (in space, without friction) are like that. Ergo, even in the case of two galaxies colliding, and their two supermassive central black holes hunting each other down and spiraling into each other (which happens due to friction), after a few billion years the merged center bulge has stabilized into the two-hole tango in a tight-and-decaying orbit ... and the rest of the stuff just sees a center of X+Y total mass, and orbits that. Thereafter, nobody cares what those two monsters do. Eventually they'll merge into a bigger monster of mass X+Y ... but this has virtually no effect on anything in orbit. Mass is mass, gravity is gravity, orbits don't change (much).
A black hole formed from core collapse is actually the remnant of a ginormous explosion (supernova). You may need a 30-solar-mass supergiant blowing its guts and outer shells off to leave behind a 5-solar-mass black hole. The remaining 25 solar masses of stuff become a lovely "planetary" nebula around it (anachronism, from before we had modern optics) -- which means they're falling outward, not inward. (We have decades-old time-lapse photos of some planetary nebulas, and we can measure them getting wider.) The black hole is thus much, much lighter (less massive) than what used to be there before -- so nearby stuff that was previously in orbit can, and does, get gravitationally ejected after a supernova (or, less violently, they just kind of drift away, like unmoored boats in a gentle tide). From far enough away, the nebula + hole still look like the same total mass -- but then maybe from those distances you weren't orbiting it anyways. If you haven't already fallen into the star while it was a 30, it's very likely that you missed your chance forever.
GR also works in the other direction! Every mass has its own Schwarzschild radius, which is easily computed by plug-and-chug. Everyday matter is way too porous, being mostly the empty gaping chasms of space between electron shells and the nuclei they orbit, so we're far bigger than our own Schwarzschild radii. But if we take any mass of any shape or size and somehow (e.g. with an Age of Non-Expansion tech ) forcibly squeeze it down to its Schwarzschild radius, then poof, it will and must collapse into a (mini-)black hole. For Earth (or any Earth-mass of any stuff), IIRC this radius is on the order of millimeters. It's only a whimsy for us in this century, but someday it could have practical applications. In fact, some of the (wacky) protests against the Large Hadron Collider are based on the far-fetched notion that it could create stable microscopic or quantum black holes. In theory, this could happen whenever you attain any energy density in a space more compact than its own Schwarzschild radius. (Remember that energy is the same as mass, hehe -- both SR and GR say that, with overwhelming evidence.) Fortunately, we've computed that LHC is too wimpy to create even the smallest allowable black hole, that black holes of that size would (1) first of all depart Earth at very nearly c, and (2) promptly blow up via Hawking radiation, and finally that cosmic rays bombard Earth's atmosphere every day with energies greater than LHC's max, and they haven't created daily showers of black holes for the last 5 billion years. So whew, we're saved by our own low tech?