Doubt regarding transferring of wordpress site to a domain

I am having a wordpress site(abc.wordpress.com) and i want to transfer it to a domain(abc.com).All the backlinks and the PR of the site will remain same or they will be down?

Plz help me out with this

Thanks in advance

this is the wrong section to post.

anyway to answer you regarding backlinks, you need to do a permanent redirect from abc.wordpress.com to domain(abc.com) to preserve them.