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This is the way I have learned to understand this situation: If Matthew Mark Lucas names his son Matthew Mark Lucas, that is Matthew Mark Lucas, Jr. Matthew Mark Lucas then becomes Matthew Mark Lucas, Sr. (only because there is a Jr.) Matthew Mark Lucas I and Matthew Mark Lucas II are considered affectations and are not proper usage. Now, if Matthew Mark Lucas names his son, say, John Charles Lucas, and John Charles Lucas names his son Matthew Mark Lucas, THAT'S Matthew Mark Lucas II. Matthew Mark Lucas may then be refered to as Matthew Mark Lucas I for purposes of differentiation, but rarely will such a person sign their name Matthew Mark Lucas I unless it is necessary to avoid confusion (as in a document where both are named parties). Even then, Matthew Mark Lucas I is unnecessary and Matthew Mark Lucas is sufficient. We're not talking royalty here. III, IV, etc., simply follow in order. If someone is named after an ancestor who was III, they may be considered IV regardless of the number of generations intervening, but such use may only be in formal situations (or where someone has a HUGE ego ;-) ).