Thanks to those of you who have answered my questions about domain transfers. I have investigated with the online site building and hosting company I want to move to and they said the following:

When it comes to transferring a domain name, it is automated which means there is no DNS needed. In fact SBI does not provide DNS. Once you sign up to SBI, you will be provided with full instructions to transfer a domain name. You will have to unlock your domain with your current host (which may take some time depending on your registrar) and once the domain is transferred, you do get notified that it has been complete.

Does this sound right. As far as unlocking my domain name gose is it a matter of calling my current hosting company or what?