No matter how you draw them, family lines are complicated. Given names are repeated and spelling is inconsistent. Family Charts are known to confuse even the smartest of rodents.
We start with two brothers who arrive with their families in the British northern colony of Nova Scotia in 1761. They probably have at least one brother arriving in the middle colonies during the same decade but that knowledge will remain a mystery to us for another two and a-half centuries. From this third brother, one and possibly more family lines first appear in the Carolinas. While their family charts may be incomplete, their genetic kinship is beyond doubt because of recent DNA testing.
Several branches can be drawn from immigrant James or William Cook down to the present day. A few are traced here; some to Cook women but mostly to Cooke men. More detail about a family or an individual may be available than appears here and you may have more information to offer about some individual or family of Cook(e)s.