If, for purposes of intestate succession, a relationship of parent and child must be established to determine succession by, through, or from a person:
(1) An adopted person is the child of an adopting parent and not of the natural parent except that adoption of a child by the spouse of a natural parent has no effect on the relationship between the child and that natural parent.
(2) In cases not covered by paragraph (1) of this section, a person born out of wedlock is a child of the mother. That person is also a child of the father, if legitimated pursuant to Chapter 13 of Title 13 or, notwithstanding any contrary provision of Chapter 13 of Title 13, if:
a. The natural parents participated in a marriage ceremony before or after the birth of the child, even though the attempted marriage is void; or
b. The paternity is established by an adjudication before the death of the father or is established thereafter by preponderance of the evidence; except, that the paternity established under this paragraph is ineffective to qualify the father or his kindred to inherit from or through the child unless the father has openly treated the child as his, and has not refused to support the child.