I know next to nothing about black holes, is there any relation between the size of a black hole and the amount of matter it's "swallowed?"
The singularity at the center doesn't grow. But a black hole's "size" generally refers to the radius of its event horizon.
Wolfram Alpha computes it for you: http://www.wolframalpha.com/input/?i=schwarzschild+radius+fo...
Mass of universe: 3 * 10^52 kg
Schwarzschild radius for that mass: 4.455 * 10^25 meters
Volume of sphere with that radius: 3.704 * 10^77 m^3
Density = mass / volume = 8.099 * 10^-29 g/cm^3, or roughly 8 times the approximate universe density
I think it's interesting that a universe-sized black hole would be a mass within an order of magnitude of the universe's mass.