third cousin.
The grandchild of your grandmother's first cousin is your third cousin. The grandchild of your grandmother's second cousin is your fourth cousin. The grandchild of your grandmother's third cousin is your fifth cousin.
Your first cousin's grandchild is your first cousin, twice removed.
Your cousin.
Your first cousin's grandchild is your first cousin, twice removed. Your second cousin's grandchild is your second cousin, twice removed. If you start looking a grandchild of a first cousin once removed, a third cousin twice removed, etc., the answer becomes more complex and depends on whether you are a member of teh younger or older generation in the relationship.
Third Cousin.
Your uncle's child is your first cousin. His grandchild is your first cousin, once removed. You are also that grandchild's first cousin, once removed.
Your father's first cousin's grandchild is your second cousin, once removed. Your father's second cousin's grandchild is your third cousin, once removed. Your father's third cousin's grandchild is your fourth cousin, once removed. And so forth.
Your great uncle's grandchild is your second cousin.
Your uncle's grandchild would be your second cousin because his grown son or daughter would be your first cousin.
You and your first cousin's grandson are first cousins, twice removed, to each other.
Your first cousin's grandchild is your first cousin twice removed
The child of your parent's first cousin is your second cousin. The grandchild of your parent's first cousin in the child of your second cousin and thus your second cousin, once removed.If you are starting with your parent's second cousin, then the grandchild is your third cousin, once removed.