False titles of nobility

False titles of nobility are titles of nobility which are fake. They have been invented or taken by a person or family. They are not recognised by the present or past government of the country. 
There are a number of schemes that pretend to confer or sell such titles. They have flourished by use of the internet. 
Self-styled titles.
In monarchies, genuine titles do exist. But they may no longer be recognised by a successor state (such as a republic). Such is the case with French titles, for example. Formerly noble families often still use their old titles, and this is generally acceptable in that society. The title is borne or claimed by a hereditary heir. That is different from an invented or falsely-attributed noble title which is claimed without any historic basis.
Self-assumption of a title is not necessarily illegal. It depends on the law in the particular country. The bearers of some self-assumed titles do not claim that the titles have been recognized by any nation at any time. 
Some individuals, associations or companies pretend to give a legal or official right to a title, to an individual or family. Naturally, this requires a remittance or donation, and hence the transaction may be illegal. Also, pretending to be a titled person with intent to deceive also may be an offence.