CainIV - 6:17 am on Jul 16, 2010 (gmt 0)
Ok, well here goes...
A while back (circa 3 years ago) we hired a development team to build out a series of websites for us. The framework was a custom code 'local directory' framework which rewrote se-friendly urls from the db dynamically.
At the time, this question came up, and it was a significant enough issue within this particular IT team that it warranted some research (and since the frameworks would not be ready and finalized in dev for at least three months, I had some time to test the theory myself.
I created a control test whereby I created two almost identical websites (approximately 50 pages), in the same niche, on the same host but on different c class ips. Title tags were, for the most part, almost identical with slight variations.
One website was built entirely with relative links and one was not. All internal linking was 'very' close to the same.
I indexed the websites and revisited my little test.
What I found was that the absolute link website was leading - by a margin, but not by enough to conclude anything.
So I pointed links from the exact same sources to both websites using the same anchor text and pointing at the (relatively) same pages.
What I found was that once links were pointed at the websites in the same fashion, both improved, but the absolute link website improved immensely more than the relative links website.
What is more interesting, is that I then began removing links to the website using absolute links, and still it outperformed the other.
I believe Google weighs on both a domain and page level. And I believe that when Google sees a link pointed at another page using the entire absolute url, it counts that as a full page reference and passes appropriate weight.
When it follows an absolute url when spidering internal links, it "sees" the reference vote the same for the destination page, it counts the reference the same as it would a link from another website assuming (and especially when) that the referring page (on your website) has inbound links to it.
When it spiders and follows a relative url internally on the same domain, it treats it as a direct reference to a 'sister' or sibling page as opposed to a 'page level' entity.
The reason why you cannot then simply internally link with absolute links and no inbound links and expect huge results is that those pages also need to be fed with inbound links, and once they are, Google treats them in this respect like they would any other page on the Internet.
A good example of this the barrage of mashup / content algo websites that massively interlink and gain significant results on less link equity.
I have tested this as well using keyword anchors linking "home" in a domain using relative links (/index.html) and using absolute links and have seen the same results where the absolute version always performed better.
Again, it is my theory only...and apart from the control tests we can do, difficult to prove.
Definitely open to debate and discussion!