Has Google ever published or has anybody ever calculated how much PageRank juice follows from one page linking to another?For example, if I have a page about cats with a PR of 3 and I link to someone else's page about cats (i.e. relevant category) then the target page will get some PR benefit from that link. What percentage of the linking page do they get? 
PageRank flow percentage
google;pagerank
The PR that is passed through a link is (PR of the page / # of links on the page) * dampening factor The dampening factor was originally .85 although it is likely that has changed since then. Also keep in mind that although PR is cumulative, the calculation of PR iterates until PR flattens (I believe to 1. You'll need to read the actual formula or summary of what it means to understand that). Basically it's impossible to determine what the PR of a page will be as the number of pages indexed by Google influences every page's final PR.FYI, relevance has nothing to with PR. PR is a numerical representation of link popularity only.