Psychological/De Facto Parent Doctrine:

A commenter on the Vermont/Virginia child custody determination thread asks: "So what is the relationship between claimed parent Janet and IMJ if not Janet's 'civil union' with Lisa?"The Vermont court was relying in large measure on what is sometimes called the "de facto parent" or "psychological parent" doctrine, which applies not just to same-sex partners, but also to the biological parent's opposite-sex boyfriend/girlfriend (or to the child's stepparent).

The doctrine is recognized not just in crunchy granola places like California and Vermont, but also Alaska, Maine, South Carolina, West Virginia, and Wisconsin (and, I'm sure, other states -- I just don't have a list handy). See, for instance Middleton v. Johnson, 2006 WL 1814177 (S.C. App. 2006), and the cases cited therein; here's the test that the South Carolina case adopts, following a Wisconsin precedent:

[T]he petitioner must show ... (1) that the biological or adoptive parent[s] consented to, and fostered, the petitioner's formation and establishment of a parent-like relationship with the child; (2) that the petitioner and the child lived together in the same household; (3) that the petitioner assumed obligations of parenthood by taking significant responsibility for the child's care, education and development, including contributing towards the child's support, without expectation of financial compensation; [and] (4) that the petitioner has been in a parental role for a length of time sufficient to have established with the child a bonded, dependent relationship parental in nature.
Factor 4 suggests that the doctrine would apply more strongly for older children, and I don't know how often it has in fact been applied as to children who are a year and a half old at the time of the breakup; but it seems a comfortable fit in such cases, too.