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Rounded corners: the root of all evil
1) Create a simple precomp. Just a solid.
2) In the main comp, put a rectangle mask on your precomp layer.
You will see one pixel worth of transition.
3) In the main comp, put a rounded mask on your precomp layer.
You will see two or more pixels worth of transition.
4) Scale it. You will see AE use even more pixels for transitions.
N.B., this does not happen if you put a mask on a solid in your main comp.
Why does AE treat masks on precomps differently?