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When a new user registers on a website, the system assigns to them a default avatar. Later, the user can change their avatar on a page containing the My account web part, on the Personal settings tab.
Here, the system allows users to delete their avatar, upload a new one, or select a predefined avatar.
You can find a live example of this on the Community Starter site. Sign in as one of the predefined users (e.g. Turbo with blank password) and click Edit my profile in the Shortcuts menu on the right.
Users with access to the administration interface can change their avatars in the My profile application.