Far away from a black hole, its gravitational field is like that of any other object with the same mass. If, for example, our Sun were replaced by a black hole of equal mass, there would be no difference as far as the orbits of solar system objects are concerned.
However, if you get very close to a black hole, it turns out that there are no stable orbits, and anything in orbit inside that distance will rather quickly fall into the black hole.
The supermassive black hole at the center of our galaxy is only a tiny fraction of a percent of the mass of the stars in our galaxy. The mass of this black hole is a few million solar masses, while there are around 400 billion stars in our galaxy. And yet from the movements of these stars we know that the stars themselves are not orbiting one another, but are instead mostly orbiting the unseen dark matter that exists within our galaxy.
And galaxies don't expand over time. They're quite stable.