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What if I want to change the address for my existing wp site? By registering and mapping a domain, will I get the end result I want?
I have domain mapping on two of my blogs and the answer to this question above is "yes". One does not have to move their blog off free hosting here at WordPress.com when they purchase a domain.
When we purchase domain mapping it is so that all the URLs from the .wordpress.com root blog when clicked anywhere on the internet will seamlessly redirect to the same content in the post under the new domain URLs.
The pagerank and authority the blog earned was earned by the .wordpress.com URLs and belongs to them. It’s not transferable. so what that means is the domain starts from zero. In about 4 – 6 months time the content will all be re-indexed by search engines under the domain URLs and all things being equal the blog will probably have the same pagerank and authority it had prior to purchasing domain mapping. http://en.support.wordpress.com/domain-mapping/register-domain/
If you choose to move your blog onto a WordPress.org install one day this is easily done. If you’ve registered your domain through WordPress.com and now want it to point to a blog or website hosted elsewhere then you can do this by updating the nameservers. http://en.support.wordpress.com/domain-mapping/domain-management/#update-nameservers