If you are transferring your domain to Cunhost and you have an active website that is hosted by elsewhere, transferring the domain transfers the domain name itself. Transferring your domain name does not automatically transfer your website data, email accounts, etc.
So before transferring your domain name, you should move your website data (if you have an active website that needs to be transferred as well) to your Cunhost account to avoid downtime and/or losing your data.
If your old host uses cPanel, we can do a cPanel to cPanel transfer for you that will do a complete copy of your account and move it to Cunhost (this is your best option if your previous host uses cPanel).
