If you have a full web hosting account, and you are getting a MailBox Full notice or a bounceback stating that your mailbox is full, please check how you have setup your POP email account.

An issue regarding Forwarders is the most likely cause:

You do not need to have a POP3 account defined in order to add a forwarder. They're entirely separate entities, and one can exist without the other without an issue.

In other words, if you don't want to keep the mail on the local server, you do not need a POP3 account while using a forwarder. Create one POP account in your manage/add/delete area. Any other email accounts that you want to forward to your main one can be configured by clicking the Forwarders link and adding the forwarder email and sending it to your one main account.

Many people do this so they do not have to login to different Webmail accounts for each email address they use.

Mailbox Full cause:
If you setup a POP email account and a forwarder, the emails received will forward to your main email AND ALSO stay on the server in your POP email account. When the POP email account is full, you will get the Mailbox full notice.

To avoid this happening, do not setup a POP account and a Forwarder. Or login and delete emails from both the main email account and the forwarded account.

If this is confusing, open a ticket and inquire.