>> Assuming random distribution (of plane of planets),
Has there been any research on this? I have no actual insight, but I'd guess the plane of the galaxy would affect plane of stellar rotation and perhaps also planetary disk alignment.
The milky way galaxy is about 200,000 light years in diameter, but only about 200 light years thick.
Given this thickness, I imagine you'd need to look beyond the 200-light-year range to notice a significant influence of the plane of the galaxy on the distribution of stars (and planets).
This solar system orbits the galactic center every 250 million years or so; making us a young adult of around 18 Galactic years old, living in a suburb of quite a busy galaxy.
Every eighteen year-old suburbanite[1] has already been pretty well socialised by local interactions in the context of a global system of local interactions, performed massively in parallel.
[1] metaphors mixed and units of measure utterly messed-around with
I love this galactic orbit measure of things. Dinosaurs like the Iguanadon were alive ~125mya, which means that the impressive thing when looking at a fossil is not that it's old, it's that it came from the other side of the galaxy. You can go and pick up a trilobite that's coming up to its third orbit.
Yes, I know, it's still from Earth, but I do think it's a weird way of looking at dinosaur fossils.
Has there been any research on this? I have no actual insight, but I'd guess the plane of the galaxy would affect plane of stellar rotation and perhaps also planetary disk alignment.