Is there a specific mental illness for those who believe they are God or immorta!

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It is regrettably quite common. In slang, it is referred to as a Messiah Complex, but it's really just a form of schizophrenia.

Here's one:

The Cotard Delusion.

'The Cotard delusion is a rare psychiatric disorder in which a person holds a delusional belief that he or she is dead, does not exist, is putrefying or has lost their blood or internal organs. Rarely, it can include delusions of immortality.'

http://listverse.com/2007/10/13/top-10-b…

I think the other person may have misenterpreted the question. Idk for sure but probably some type of sociopathic disorder. Type in on google "god complex"

I would call that Megalomania
Megalomania is a psychopathological condition characterized by delusional fantasies of wealth, power, or greatness.

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