Well if your father and your mom's boyfriend are third cousins then you and your mom's boyfriend are third cousins once removed.
The children of your father's first cousin are your second cousins; of your father's second cousin are your third cousins; etc.
second cousins to his cousin's children, you'd be third cousins
If your father and your girlfriend's father are second cousins, then you and your girlfriend are third cousins. You share one or two great-great-grandparents.
The children of your father and the children of your father's first cousin are second cousins to each other. The children of your father and the children of your father's second cousin are third cousins to each other.
Your father's third cousin is your third cousin once removed.
You and your first cousin's children are first cousins, once removed, to each other . You and your second cousin's children are second cousins, once removed, to each other . You and your third cousin's children are third cousins, once removed, to each other .
By definition, cousins share a common ancestor. Otherwise they would not be cousins. It is common for people to refer to those that 'marry in' to the family, those that are adopted or are step children as cousins when there is really no common ancestor. Third cousins would share a common Great Great Grandparent. There is no prohibition to marriage for third cousins.
The first cousin of your dad's first cousin is also your your dad's first cousin or is not related to him or to you. The children of two first cousins are second cousins to each other. So the son of the first cousin of your dad's first cousin is either your second cousin, or is not related to you at all.
The son, or daughter, of your father's first cousin is your 2nd cousin. The son, or daughter, of your father's second cousins is your third cousin. The son, or daughter, of your father's third cousin is your fourth cousin. And so on.
She would be your second cousin.Your father's first cousin is your first cousin, once removed.The daughter of your father's first cousin is your second cousin.The daughter of your father's first cousin is your father'sfirst cousin once removed and your second cousin. Second cousins are people who have a common great grandparent. First cousins are people who have a common grandparent. Cousin relationships between people of different generations are determined with reference to the cousin who is closest to the common ancestor, and by the number of generations between the two cousins.
If his great grandmother and your grandmother are firstcousins, the you and he are third cousins, once removed.
The grandchild of your father's first cousin and your child (your father's grandchild) are third cousins to each other. In the US, no jurisdiction prohibits such marriages.