Why are all galaxies roughly the same size? what determines the stable mass of galaxies, stars, star clusters or even galaxy clusters? Is there some obvious way to determine the classes of stable mass clusters from the initial conditions of the universe. I am more interested in the abstract version of the problem in newtonian mechanics. Is it a push to say that newtonian mechanics dictates what sizes galaxies should be just because the nature of the inverse square law or even the density of mass?
 A: As dmckee points out in a comment, it is not at all true that galaxies are roughly the same size.  Galaxies may be as small as a few thousand stars or as large as trillions of stars.
On the smallest end of the range, there is no hard lower bound on the size of a galaxy.  Instead, very small "galaxies" tend to be reclassified as intergalactic globular clusters, although there is no really clear distinction between the two categories.  Small groups of stars such as Segue 1, which contains at most a few thousand stars, may be classified either way depending on their theorized origin.  This paper argues that Segue 1 is "the least luminous of the ultra-faint galaxies recently discovered around the Milky Way, and is thus the least luminous known galaxy."
The upper bound of the size range is also somewhat flexible.  The supergiant elliptical galaxy IC 1101 contains about 100 trillion stars.  However, galaxies' luminosity is limited because very bright galaxies blow away their interstellar gas through radiation pressure, preventing new stars from forming.
