The case concerned a poly family composed of two men and one woman. The woman in the trupple (three person poly relationship) gave birth to a child. The family did not know which man was the father
The law in Newfoundland did not recognize more than two parents. The judge said that there was a gap in the 30-year-old legislation, because it didn't consider poly families. The judge said it was in the best interests of the child that all three of the child's parents be recognized under the law.
This case is a significant development for poly families. In the last couple of decades, parenting cases were mostly about the recognition of same sex parents . In a 2007 Ontario case, a lesbian couple had a child which was born from a sexual relationship between one of the mothers and a male friend. In that case the court held that both of a child's mothers were parents along with the child's father. But in that case the three parents did not live together and were not in a continuing poly relationship.
In B.C., the law does provide for the recognition of three parents where there are two people and a donor of genetic material, if everyone agrees. But the law makes no general provision for the children of a trupple. So the same logic would apply to a B.C. case: there is a gap in the legislation, and all three adults in the trupple should be recognized as the parents of a child born to them.
Parents who already have children when they form a trupple cannot be legally recognized as 'parents' of their collective children, though if the trupple later broke up a court could find that it was in the best interests of the children to spend time with each of the parents.
It is theoretically possible for a court to order that all the parents in the trupple are guardians of the children (giving them most of the rights of a parent, including the right to decide a child's medical care). Or a trupple in that situation can make an agreement with each other which confers emergency guardianship on each parent with respect to all the children.
Polygamous families - more than two married spouses - are illegal in Canada, but polyamorous families - where more than two people are in conjugal relationships with each other - are not illegal.
For more information about polyamorous families, read John-Paul Boyd's article.