Re: resolution in AE

I don't think you *fully* understand him, as he has given you the answer... collapse transformations.

Precomping takes whatever is inside and kind of treats it as a new piece of footage (probably not an accurate way of describing it, for various reasons, but it might help you understand the resolution thing). So when you have made a small precomp and put it into a new one, it's now thinking of that precomp as a piece of footage with its dimensions, NOT as the source file... this is GOOD in many cases, for example it can optimise speed when you're working with a small section of an asset, but in your case you are noticing the quality loss.

Here's where Collapse Transformations comes in. Read the help page to see what it does, and then try it out :) It will allow you to get the quality you want in the final render (but it does get tricky when you combine it with 3D stuff and effects, sometimes it takes some wrangling to get what you want without side-effects).