How much of the universe will get flatter in how long?

Question

So I learned recently that star systems are relatively flat due to the conservation of angular momentum.

On how large a scale does this degree of flattening apply. i.e will the universe eventually flatten out, or galaxy clusters, or is it just star systems. At a guess, it depends on the validity of this statement:

Given enough time flattening will occur regardless of how chaotic the initial conditions of the original system is.

This is related: Why don't stars in globular clusters all orbit in the same plane?

Answer 1

An infinite universe which is approximately homogeneous should not flatten out. Flattening out is a local process, but on the large scale of homogeneity the GR gravity dynamics overwhelm the local process. The scale of flattening is generally at the galaxy level, possibly also regarding galaxy clusters. I am curious about the quote in your question, and I would very much appreciate a reference for it.