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Thanx for your feedback, Emko
2) Links of any PR can boost your own sites PR. (How else could sites like uiuc.edu get PR10? Not just by getting links from other PR10's.) Incoming links can never hurt you.
Should I rather use absolute hyperlinks on my homepage or relative? Whats better for google & page rank?
the longer the domain (url), the more characters and file size.
Use the shortest relative url possibly particularly on pages with lots of links.
If I put www.mydomain.com/mypage.htm it looks exactly the same to a spider (or surfer) once it's fetched the page as "/mypage.htm" as the domain name is automatically attached. Relative URL's are mainly useful to save coding time (and make it easier to move to a new domain name with the same site structure). I'm certain it's irrelevant for crawlers.
But, if someone else hooks up to your relative URL, that could be a different story! ;)