In the same thread, phranque also cites a discussion about CainIV's test which suggests that absolute links may be better for SEO. The consensus has generally been that absolute links and root relative links are basically equal for SEO... but that relative links that aren't root relative should be avoided.
Also not clear in your post...
absolute links www.mydomainname.com
Note that links beginning with www are not absolute links, as they don't include the (http) protocol. I've seen some sites get into quite a bit of trouble using www at the start of an internal nav url, as this can look like the beginning of a relative link (of the kind that isn't root relative), which can create a very messy url.