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Stavros, PageRank can indeed hint at site's strength - many authoritative sites exhibit very high PageRank values and going up against them may be silly in some cases. However it's a workable situation... If you see a site with PageRank 10 in the results yet their site lacks the phrase you're targeting in essential places such as title tag, content and inbound links (as part of anchor text) it may in fact be possible to beat them. Basically relevance will beat authority. That's why Microsoft doesn't rank well for "Men's Shoes" despite their high PR. Also PageRank is a raw importance value assigned to each individual page not to a phrase or other factors and is transmitted through links. One page gives other page it's PageRank by linking to it. Hope this answers your question.