There are a number of good partial answers here, and a few good total ones, as well as a few misleading statements.
First, let's dispense with the expansion of the universe as having any effect on the galaxy. Do a little math, and you can see this. The current best estimate of the Hubble expansion parameter, H0, is in the neighborhood of 72 km/s/Mpc (kilometers per second per megaparsec). Across the entire galaxy, a distance, D, of about 100 k lt-y, or 30 kpc = 0.03 Mpc, the total effect, as a velocity difference, of that expansion rate, amounts to
∆v = H0*D = 2.2 km/s
The orbital velocity of stars about the galactic center, once you get away from the central bulge, is a fairly uniform 210 - 240 km/s, or more than 100 times the Hubble expansion rate. In short, the motions of stars within any galaxy due to mutual gravitation, completely dominate any effect due to universal expansion. This is still true on the scale of galactic clusters. In fact, the Andromeda Galaxy, M31, is actually *approaching* our Milky Way (they and we are the two largest galaxies in our Local Cluster).
Next, Vincent G's statement that at any decent distance from a black hole (BH), its gravitating effects are just those of any compact object of the same mass, is totally correct. It's only when you get very close to the event horizon, or, for a rotating BH, the static limit, that things get crazy. Matter that gets that close, tends to wind up *joining* the BH (RIP).
And, yes, it is widely thought that there is a supermassive BH at the center of the galaxy, and no, the stars are not all floating away from it, nor are they "spreading out over time." They're following their regular orbits around the center. I know that a lot of popular portrayals of BH's make them out to be some sort of giant super-vac, sucking in everything in creation, but that isn't how they work, even in theory (and BH's really are in the theory stage at present, because by their very nature, if they exist, they would be nearly impossible to detect directly -- we have to rely on lots of other kinds of evidence for them, and it is quite substantial -- many things that we see, if not caused by BH's, would have to have even more exotic explanations).