Once you've got yourself a radio.net account and have signed in, any favorites you save will be stored on your account. When you sign in to this account on another computer or laptop on the radio.net website, you'll be able to find your favorites right where you left them. In the same way, any changes made to your favorites (removing or rearranging) will be saved to your account.
Please mind that the login has been removed in the apps for Android and iOS in version 5.x. So syncing the favorites between a) the radio.net website and the app(s), b) between Android and iOS and c) on several Android devices is no longer possible. On iOS devices the favorites are being synced via iCloud.