Who is a widow's next of kin?

That depends on whether or not they have any children, grandchildren, siblings, or if their parents are still living. If they have children, then the children are the next of kin. If they had children and the children are deceased, yet had children of their own, then the grandchildren would be the next of kin.

If there are no grandchildren either, then the parents are next of kin. If the parents are deceased, then the siblings would be next of kin. If they have no children, grandchildren, siblings or surviving parents or grandparents, then the closest blood relatives would be their next of kin, such as aunts and uncles, cousins, etc. in that order.