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The best method of dealing with a problem user is not to delete the account. It is better to simply block them from logging in. This is true for a few different reasons.
First, it is temporary, so it can be used to suspend rather than ban. Second, if you are requiring your users to authenticate via email and you are not allowing duplicate email addresses, it will make it slightly more difficult for them to simply recreate their account or create a new account.
While there are some extensions that will allow for blocking by IP address, Joomla! does not include this functionality by default. Additionally, please note that as discussed in the Security and Performance FAQs,this method is not recommended because it is ineffective. First, because the problem user may not actually be the owner of the IP address. Second, because most IP addresses are non-static, so they will change periodically. For example, if the person is using a wireless laptop, and simply moves to a different wireless router, they will end up with a new IP address.