hi
What happen to the PR of the home page when the domain that register with the .com and now changed to .org.

PR is relative to links pointing to specific pages so if the domain is different, the pages are different so there would be no relationship between the pr of .com and the .org.

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Let us take an Example that if the Site having the URL http://www.aaa.com having the PR 5 and if in the Future the URL of the Site Changed to http://www.aaa.org . Will the PR Changes at this Point.

Like Dilligaf said, the PR of www.aaa.org will have nothing to do with the site www.aaa.com since they are two different sites. If you trash the .com to open the .org, you have to redirect all traffic with a 301 redirection and get all the links pointing to the .com to be changed to point to the .org

They are two different sites that the pages have different page ID's, each page ID is specific to the page in the google index... Only getting links to a page will raise it's PR.