What happens if my parents do not specify a benefactor?

If you were adopted by your parents, then the law treats you as though you were born naturally to them. I'm not sure I understand what you mean by saying that they did not specify a "benefactor" (I think you mean "beneficiary"?) in their will - this is one of the primary purposes of the will, so if they executed one, there should be some guidance about how they wish for their estates to pass. If there is no will (or no mention of beneficiary designation in their will), then the statutory distribution would control - generally, this means that the surviving spouse inherits. If there is no surviving spouse, then the child/children inherit, etc. If you are their legal child and you survive your parents, then you would be the one in line to claim their estate (siblings are not in line to inherit if there are surviving children), unless their will (or other beneficiary/transfer designation provides otherwise).