Which system process do I block from the internet to prevent ads from showing up? Yes, this is similar to my own previous question on the subject.
I'm being very specific here though - despite having wrapped ad blocking with hosts file and firewall, some apps (several more now) are able to merrily display banner ads even when they are explicitly blocked from connecting to the net. My firewall (Droidwall) works, because if I block a legitimate app it gets blocked.

How are they doing this?? Is there some Google made common system process that they access?
Such ads are not fetched from the internet, they are built into the app. Usually the ads would feature some other app from the same developer.