I can kind of see what you are trying to do there. As far as noise issues go, the 7812 and LM317 are not very high-speed devices, and they certainly don’t give the complications of switching regulators. For your application, what kind of noise are you especially trying to get away from?
I know you’re not doing a switching regulator, but depending on what you’re powering that has you concerned about noise, the following might be helpful.
Grounding, shielding, and ground planes are a complex subject, and what applies in high-impedance, low-frequency circuits like audio is not the same as what applies in low-impedance, high-frequency circuits like RF, digital, and switching regulators. What probably escapes the hobbyist most is that in the latter, the ground return current does not follow the shortest & widest path, but instead, mutual inductance makes it travel directly under the trace whose current it is returning, taking on the shape of the trace, so there is equal an oposite current flow in the two directions, effectively making it a balanced circuit. This minimizes inductance as well as unwanted stray coupling. For this reason, copper pours and ground fills do not qualify as a ground plane, as they do not provide a continuous return path under a trace.
As for the star, the center of a star should be the place that matters most, like the ground pin of a switching regulator IC, or of a data converter. Having the center at some irrelevant place out in the middle of nowhere is generally not very helpful. Even in the case of just feeding power, it should be the power source and be well bypassed to ground right there.
If there are separate planes on a board separating something like digital from analog circuits to keep digital noise out of the analog, and the grounds are joined in one place, any traces that go from one circuit to the other should cross the barrier only at the place where the planes are joined, not out where there’s a cut between the planes, and there should be a bypass capacitor on the power right there at the junction.
When I design switching regulator circuits, I always add ferrite beads at the input and output to help keep the high-frequency noise out of other circuits. Layout for switching regulators is very critical.