The game has several options for logging in and out. Learn more in this article.
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You can sign up for the game using either an email address and password or a social network account (Google or Facebook). The method you use to sign up becomes your default login method.
To log out of the game, go to the Menu by clicking three lines in the upper-right corner of the game tab, scroll down, and select the preferred option. You can either log out of your current device or all your devices.
Your Hero Wars: Dominion Era account is linked to your Facebook account. To log in to / log out of the game, you need to log in / log out of your Facebook page.
To get detailed instructions, check these articles in the Facebook Help Center: Log in to your Facebook account and How to log out of Facebook.