You can figure out alot by the patents google has. Google gives more weight to links with similar content. Anyone could get thousands of links to a website but not evey site can get thousands of high ranking links from similar sites.
It should also be a given that related content links generate better traffic. If I am visiting a site that explains how to fix my truck, I'm sure as hell not clicking on that pet care link, though I might click on that ford banner. Likewise, if I am reading up on how to get my cat to stop shredding my curtains I likely wont be clicking the ad for a discount oil change for my pick-up (mainly cuz I don't have a truck). While every link counts to some degree, some are naturally more important then others, and I'm not just talking about googles PR...and if you are, then you may be missing out on some quality traffic.
Not seen proof of this - anyhow too many people try to second guess google. Many people have different experiences with them and many manage to evade what others are experiencing! Who will ever know why! .
google has a patent for this, but there is no evidence that they actually use it. Plus, I've read one prominent SEO that says forget relevance, the same old things are still important: trust, authority, PR.
No. There is no proof (the original patent is a bit old, so I'm not sure that counts). If someone can prove it - show us! I'll gladly admit I was wrong. I'm actually working under the assumption that it IS correct lately in my link building, but... I suspect it's not all that cut and dried.
Well im first for a very competitive word at the moment. It took me less links and less time to get there because i only bothered with backlinks from related sites. This is not the first time iv done it either.