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I'm having trouble with my current host who doesn't answer technical and domain related questions, so I'm thinking of moving.
The trouble is I purchased the domain from them, when I purchased the hosting and they seem to have special powers that prevent it from being transferred.
Of course I searched around already, but everyone seems to have a different take.
Could someone give me an idea of what I need to do?
Pick another registrar (there are many). Go to the "transfer domains" section of that registrar's site. Proceed with transferring your domain to that registrar. You'll start to receive emails from both registrars asking you to approve the transfer. You'll need to login wherever they say to do this. It should take a few business days for everything to get done.
There are a few squirrelly things that could happen along the way. NSI makes you get an "auth code" which you can only get by calling them. You may also need to access your current registrar's account to "unlock" the domain so the transfer will proceed. You (or your current registrar) may have locked the domain to prevent unwanted transfers.
Exactly what happens depends on who the losing and winning registrars are, because each registrar has a slightly different process.
They are different beasts and require different actions. Clarifying the question will help with the answers.