Usually almost nothing on a good engine. And the name is HIGHLY misleading. They are ABSOLUTELY NOT "Air/Oil Separators" - they are "Air/Liquid Separators" and the distinction is very relevant since engines produce large amounts of condensation during warm up. This is generally directed into the cylinders and burnt by the stock breather system. In an AOS it is saved and mixed with the normal small amount of oil vapor to produce a nasty concoction of milkshake-esque sludge that coats and restricts the normal operation of the PCV and breather system.
It is honestly a horrible idea for a street vehicle. Catch cans and AOSs are RACE CAR parts. They can serve a function in a racing environment to solve specific problems related to ulta-high performance engines. These are engines that see intermittent use and have highly accelerated maintenance requirements - part of which is to clean and service these accessory systems to prevent clogging and empty collection vessels, etc. These are NOT appropriate for street use.
GD