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Theory...
widget.com (pr6) links to blackberries.com and it becomes a pr6 as well. However, blackberries.com has low ranking for its targeted keywords which are very different to widget.com.
BUT
widget.com links to bluewidget.com and this site gets pr6 and does very well for its targeted keywords.
Conclusion:
Off theme links can generate a high pr for your site, but this is useless for ranking, you may just as well have pr0. On theme links generate on theme pr for relevant ranking.
So there is two aspects to PR. One is the overall value shown by the toolbar which is pretty meaningless and then their is a hidden pr value calculated by the amount and quality of on theme links in. This would explain why some high pr sites perform very badly.... they have few on theme pr coming in, having acquired their pr from an unrelated source.
There seems to be something in the 'similar pages' that is the key...
Themeing would not be all that difficult to program. In fact it would be quite easy. It would be very computationally intensive to do for 3 billion pages though. It just requires doing some statistical analysis of the words used in the pages that come up for a keyword, and then doing the same for the the pages that point to those pages and compare the two.
An even easier and quicker method, would be to give extra weight to links from pages that rank high in the same search. If all the top ranking widget sites link to you, then you are obviously important, even if your PR is not as high as some other sites. That is how easy themeing can be.
Krishna Bharat's and George Mihaila's approach is intereesting, in "Hilltop: A Search Engine based on Expert Documents". I don't think that the "Detecting Host Affiliation" section would work well but their description of "Expert Lookup" followed by "Target Ranking" seems like a nice approach to reducing the computational overhead that FRG mentions (GoogleGuy has hinted at hub & authority in the past).
PR is not themed if your page has a PR7 and links to another page it will pass on exactly the same a mount of PR, weather the site is similar/related or not.
As for theming - I believe it is happening
Back-links from sites in the same DMOZ cat as your site is one example.
widget.com links to bluewidget.com and this site gets pr6 and does very well for its targeted keywords.
Isn't it equally possible (and more likely) that bluewidgets.com is simply coming up higher for its targeted keywords because it has more relevant content on the page?
If the page is (a) relevant to the search query and (b) has a healthy new dose of incoming PageRank to give it a boost, it should do very well even if Google isn't using "theming" per se.
Personal experience concerns two directory sites with the same structure, just different themes. The one with on theme 'links in' does very well, the other very much less so. Style of content and amount of text per page is almost the same, so you would expect some correlation.
Competition from other sites could be a factor in the serps, and of course number of people searching for either subject. However the less popular site should be doing well.... and isn't!. I suspect the linking theme is now a factor. Links in from pages with on theme meta titles etc. seem to count for a lot, almost as much as anchor text. I suspect a page called "links" may carry high pr but be little benefit in helping you achieve good ranking, whereas a page called 'widgets' with a link to your widget site is worth a lot, even if it is carrying only a small amount of pr. Add to this overall linking site theme and the benefits start to stack up.
I would personally now prefer a link from a pr5 on theme than 20 pr6 off theme..... the google tool bar is becoming a red herring.
