well, no.. the domain is at GoDummy, oops
, sorry, GoDaddy
and it will stay there for ever[lets say].
However, since you control the domain [pay rent to the registrar],
you can point it,
forward it,
host it
[or whatever]
on any server you desire that is connected to the internet.
the domain [example.com] is a 'registered' name, and you point it at what ever 'phone-number' [server-URL] you want, the web site is the answering machine, when the internet user dials up your number [server-URL], the web site answers with all your cool stuff.
Neat
you can use nameserver(s) [ns1.example.com,ns2.example.com] to point the name..
or forward the name to the directory on a server
http://user-name.example.com/
edit.. there is lots of crud i could add, but you can google this subject and read for weeks,, lol
i think i tend to get into info overload sometimes, what if this or what if that....