When to repoint name servers to new host?

Let's say that I have a domain name and website both on GoDaddy. I have just initiated a domain name transfer to HostGator. I have uploaded my new site to HostGator by FTPing to an IP address. I have set up the domain name email on HostGator.

GoDaddy has not released the domain name yet. Can I at this time have HostGator point the name servers to HostGator servers? Or do I need to wait for the domain name transfer to complete before pointing the name servers?

Who owns these name servers anyway? Does Godaddy have their own name servers and Host Gator have their own name server? Or are name servers consider separate entities not under the direct ownership of webhosts?

They each have their own name servers. I don't know what the Terms Of Service are when it comes to the move.

As far as I know- it should go over on the same ns as it was on before you began the transfer. So it can be an idea to point ns to where you want, before starting the transfer.

I doubt they will do anything untill the domain if moved.