Fake page rank is a trick used by some, to fool googlebot by using 301 permanent redirect method to display invalid pagerank for a webpage.

How does it works ?

When a search engine bot visits a website, it is redirected to webpage with high pagerank, so bot assigns high page rank to page that redirected assuming both are same.
However when a human visits the website he is not redirected and so he sees fake pagerank of redirected website in pagerank toolbar.

To detect if particular website or blog has fake pagerank, visit free fakepagerankchecker tool and put down your website URL and hit "Check Pagerank" button.

Blogpandit find fake pagerank for blog or website

You may even add multiple domain or website URL in that box to find bulk page rank at a time.
You would then see the result showing the current page rank for each domain and there validity status.

check fake pagerank for blog or website Blogpandit

Never use this method to fake page rank, as it can risk your domain page rank future if caught by Google for cloaking.