A parent-child relationship is established between a person and a child if:

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(1) The person gives birth to the child, except as otherwise provided in sections 46b-521 to 46b-538, inclusive;

(2) There is a presumption under subdivision (1) or (2) of subsection (a) of section 46b-488 of the person’s parentage of the child, unless the presumption is overcome in a judicial proceeding;

(3) There is a presumption under subdivision (3) of subsection (a) of section 46b-488, and the person is adjudicated a parent of the child or acknowledges parentage of the child under sections 46b-476 to 46b-487, inclusive;

(4) The person is adjudicated a parent of the child under section 46b-490;

(5) The person is adjudicated a parent of the child under sections 46b-495 to 46b-505, inclusive;

(6) The person adopts the child;

(7) The person acknowledges parentage of the child under sections 46b-476 to 46b-487, inclusive, unless the acknowledgment is rescinded under section 46b-482 or successfully challenged under section 46b-483;

(8) The person’s parentage of the child is established under sections 46b-509 to 46b-517, inclusive;

(9) The person’s parentage of the child is established under sections 46b-521 to 46b-538, inclusive; or

(10) The court is deemed to have made an adjudication of parentage pursuant to subsection (b) of section 46b-468.