"Advertise on this site" questions

Hi,

I noticed that many sites which carry adsense offer a link "advertise on this site" in their google adsense boxes. Does that mean that I can specifically focus on this particular site to show my adwords?

I want to work in a few very tiny niches. Can I simply pick the sites I want my adwords to be served, check if they do adsense and then have my adwords served exactly on this site?

And from an website owner perspective serving adsense myself: Imagine if I encourage and stress that potential advertisers should put their adwords on my site through Google? If there are companies doing that over a longer period of time successfully, I could later make them a sponsor of my site directly without Google.

Would you think that's practical?

Looking forward to hear your opinions.

Ben

I wrote a little blog post about this a while back.

http://www.fishseo.com/blog/2006/02/14/if-you-use-adsense-you-must-read-this/