The creator of any work on facebook would normally be the owner of the copyright.
The important question with facebook is who has rights to control what's done with the copyrighted material.
If you go to the Facebook privacy policy at
http://www.facebook.com/policy.php, that leads you to their Statement of Rights and Responsibilities at
http://www.facebook.com/policy.php#!/terms.php .
There, you will find the following, current as of 2/1/11 (but subject to revision when they like):
"
Sharing Your Content and InformationYou own all of the content and information you post on Facebook, and you can control how it is shared through your privacy and application settings."
Nice, so far, but read on....
"For content that is covered by intellectual property rights, like photos and videos ("IP content") [and they don't say it, but what you write is also covered by IP rights],
you specifically give us the following permission, subject to your privacy and application settings: you grant us a non-exclusive, transferable, sub-licensable, royalty-free, worldwide license to use any IP content that you post on or in connection with Facebook ("IP License"). This IP License ends when you delete your IP content or your account unless your content has been shared with others, and they have not deleted it." [Emphasis added.]
So, so long as something you post remains on facebook, whether on your page
or someone else's, you've given facebook permission to use it, sub-license it, transfer it to someone else, what-have-you, for free.
Presumably, facebook is not intending to sell copies of your work and the above is intended to be a cya clause to protect facebook from other peoples' misdeeds with your copyrighted material. Nevertheless, the fact remains that so long as any work you've a copyright in remains on facebook you cannot offer anyone an exclusive license on that work.
So if you have something whose IP rights you want to maintain control over, it's best not to post it on facebook.