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The actual process for transferring your domain will vary depending on which service you are transferring to. Make sure that you read the instructions for transferring posted on the new registrar's support pages for exact instructions. You will likely need to create an account with the registrar before you can access this page. You can usually find the Transfer Domain section in the control panel for your new registrar, or you may be given the option to start the process when you create your account. You may need to contact the registrar's support staff to initiate a transfer if there is no option available on the website. Make sure to include the TLD (.com, .net, .org, etc.). You may be able to transfer multiple domains at once. You do not need to include the www. part of the address. When asked, enter in the code that you received from your old registrar. Make sure that you enter the code exactly, or else the transfer will not process properly. You will be contacted by your old registrar asking if you authorize the transfer. You will be either emailed or called, using the information you have provided to your old registrar. This is where having the correct contact information is important. If you are not registered as the owner of the domain, you will not be able to be contacted about the transfer even if you are the actual owner. You usually will need to pay for your domain to be transferred. Some services require that you automatically renew for an additional year when you transfer. You may be able to get a free transfer for signing up with the new registrar. Your new registrar will configure DNS and name servers for you once the transfer has been authorized. After the transfer has been set up by the new registrar, it can take up to a few days for your DNS changes to be recognized worldwide. Your website should still be available. The actual process will vary depending on the registrar you choose. This may include an extra round of authentication from the new registrar. Check the support pages for the new registrar for details. Some domain registrars allow you to mask your domain registration information so that your contact information is not available to the general public when a WHOIS search is performed. Instead, the registrar's information will be displayed, hiding your name, phone number, address, and email. Usually, private registration costs extra. Once the transfer is complete, you can cancel your service with your old registrar. Make sure that the transfer was completely successful before doing so, or your website may go down until the transfer goes into effect worldwide.

Summary:
Read the support pages for your new registrar. Visit the transfer page for the new registrar. Enter in the domain you are transferring. Enter in your Authorization Code. Verify that you are authorizing the transfer. Pay for the transfer. Wait for your settings to transfer. Decide if you want a private domain. Cancel your old service.