Well if you register it an its registered under you or your organization then you essentially own the domain. The only possible diversion from this i could think of is if you use one of those anonymous registration features - then typically the compnay your going through puts thier info down for the Admin/Owner i think - but even then i would think you are still the owner unless ofcourse you let the registration expire then its entirely possible they reregister it in thier name and take possesion. But ive never run accross that. Perosnally i liek to keep all my domian info with my host as it makes for much easier administration - ofcoure i do pay a premium for this as my host charge like $15 biannually and i could go with somewher eliek godaddy or something and get a much cheaper rate... but thats one more login,control panel, point of contact, etc. i have to keep track of. To me its worth the cost.

Now to answer his original question - theres a coupel ways you can go about it depending on what the company youre with offers:

1.) Transfer the domain to a new registrar - This will transfer the domain to another company for registration/renewal. Typically there is a fee fro this from either the current registrar, or the new registrar (sometimes both) equal to the cost of a new registration. But it will allow you to totally cut ties to the current company you are using. Everyones process is a tad different but the basic steps are to unlock the domian, initiate the transfer, approve the transfer, and then wait till the new record propagates.

2.) Change your name servers - If youre happy with the current company as far as registration and dns goes then you could just cancel your hosting account with them but keep the domin name account open and change your nameservers. Most companies offer this if they also offer domain parking and registration as standalone services. To do this you would open your hosting accoutn ith the new company. They will provide you with nameservers. You would go to your current host and then update your nameserver to those provided by the new company. Then jsut wait for the record to propagate.

3.) Point to another server (not recommended) - In this case if your hsot offers it you can point your domain to another server by using DNS record. Im not really going to go into this because it really shouldnt be used with tld's but rather just subdomains (like if you host your email elsewhere or a webDAV server or SVN repository or something).