Below are all the current options. Please pick the one that suits your situation. 

 

IOS to IOSChoosing the same login.
IOS to AndroidIf Apple account email is hidden - you can’t move to Android. If Email is enabled and a Gmail, you should be able to login via Google. Facebook login is also available on both.
IOS to BrowserIf Apple account email is hidden - you can’t move to Browser. If Email is enabled, you should be able to sign up with same email and set a password.
Android to AndroidChoosing the same login.
Android to IOSGPG can’t be transferred. Facebook and Google are available to login.
Android to BrowserGPG can’t be transferred. Gmail: you should be able to sign up with same email and set a password. If you have Facebook sign-in with an enabled email - you can login the same way as Google email.
Browser to BrowserChoosing the same login.
Browser to IOSIf you signed-up on Browser with Gmail you can use the Gmail login. If signed up with the same email that is connected to your facebook, you should be able to login with Facebook. Other options are unavailable.
Browser to AndroidIf you signed-up on Browser with Gmail you can use the Gmail login. If signed up with the same email that is connected to your facebook, you should be able to login with Facebook. Other options are unavailable.
Just Play to transferNot yet available. Tied to specific device only.
Steam to IOSNot yet available.
Steam to AndroidNot yet available.
Steam to BrowserNot yet available.
Facebook to IOSYou can use the Facebook login method if also logged in to the same Facebook on your device.
Facebook to AndroidYou can use the Facebook login method if also logged in to the same Facebook on your device.
Facebook to BrowserIf the email is not hidden, you can sign up with your Facebook email and create a password. Sadly, if hidden - you do not have access to browser and will need to use the Facebook logins on mobile.