Did you know there's a big difference between owning your domain name (bbc.co.uk, etc) and the technical configuration.
In simple terms - one is legal and your Intellectual Property on the internet and the other is purely technical stuff to make your email and website work.
NEVER EVER let your domain name then fall into the hands of another! Web developers in particular are very fond of lifting this out of your control BUT if they do - your whole business online presence is in their hands and it can be thousands of pounds to get back.
You also though need to be careful of business partners and if you do decide to lodge with a third party THEN ensure that the address and registrant details are all set to be you. Better if in the hand of one trusted partner and THERE IS NEVER any need for someone to take this from you.