A parent-child relationship is established between a person and a child if:
(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person acknowledges parentage of the child under sections 46b-476 to 46b-487 , inclusive, unless the acknowledgment is rescinded under section 46b-482 or successfully challenged under section 46b-483 ;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 .