Okla. Stat. tit. 84, § 84-215: Inheritance by and from illegitimate child

For inheritance purposes, a child born out of wedlock stands in

the same relation to his mother and her kindred, and she and her

kindred to the child, as if that child had been born in wedlock. For

like purposes, every such child stands in identical relation to his

father and his kindred, and the latter and his kindred to the child,

whenever: (a) the father, in writing, signed in the presence of a

competent witness acknowledges himself to be the father of the

child, (b) the father and mother intermarried subsequent to the

child's birth, and the father, after such marriage, acknowledged the

child as his own or adopted him into his family, (c) the father

publicly acknowledged such child as his own, receiving it as such,

with the consent of his wife, if he is married, into his family and

otherwise treating it as if it were a child born in wedlock, or (d)

the father was judicially determined to be such in a paternity

proceeding before a court of competent jurisdiction.

For all purposes, the issue of all marriages null in law, or

dissolved by divorce, are deemed to have been born in wedlock.