If you use web hosting where the provider has specified the amount of space available, junk emails can cause the space to fill up quickly. Some hosting providers like Hostgator also specify the maximum number of inodes you can have in a shared hosting account, and each email corresponds to separate inode.
In Cpanel , you can disable catch all by setting default ID to :fail: no such user here
For reseller / VPS/ dedicated server, you can also login to the WHM >> Tweak Settings and set “Default catch-all/default address behavior for new accounts. fail is usually the best choice if you are getting mail attacks.