Maryland

What is the name of your state?Maryland

In the state of Maryland - if a father walked out on his child when the child was 10yrs of age, no contact since that time, unknown whereabouts of father, and this child is now 40plus, and the father dies, is this child entitled to sue his estate for back support?

Any unpaid arrearage would belong to the mother of that child. If she never obtained a CO, there is no arrearage. And, if there was an order, some states have statutes of limitations, so it would depend up what court actions to collect were taken by the CP.