I was curious if you had to actually _own_ the site that you had your adwords account on?

ie. Friend runs a site and doesn't mind placing your adwords on his/her site.

ie. You offer free hosting to users and in return they place your adwords on their main page.

I'm sure this is a simple question but I was unable to find it with a search.

No it dosent need to be specifically your site as such, however you do need to have control over it.

I would read the google TOS beforehand though.