(a) The mother-child relationship may be established between a woman and a child by:

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(1) the woman’s having given birth to the child;
(2) an adjudication of the woman’s maternity; or
(3) adoption of the child by the woman.
(b) The father-child relationship may be established between a man and a child by:

(1) an unrebutted presumption of the man’s paternity of the child under Section 26-17-204;
(2) an effective acknowledgment of paternity by the man under Article 3, unless the acknowledgment has been rescinded or successfully challenged;
(3) an adjudication of the man’s paternity;
(4) adoption of the child by the man; or
(5) the man’s having consented to assisted reproduction by a woman under Article 7 which resulted in the birth of the child.