At the time, Ms Parsons was just starting a relationship with her future wife Margaret Parsons.

Mr Masson has said he believed he was fathering a child whom he would help parent, through financial support and physical care.

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He was known as "daddy" to both the girl and her younger sister, who was not his biological daughter, and he was heavily involved from the beginning, volunteering at the school canteen and taking her to ballet lessons.

The legal dispute between the man and the women erupted when the Parsons attempted to take the girls, then aged 10 and 9, to live in New Zealand, where the couple married in 2015.

Mr Masson was at first successful in fighting their move overseas, but the Parsons appealed before a full court of the Family Court, which agreed with the women that he was not a legal parent.

Mr Masson appealed to the High Court where the case was heard in Canberra on Tuesday.

Mr Masson argued that the women's construction of the law would leave the child with no parents, as the child would not be captured by the state law's parenthood provisions about the status of children conceived by artificial insemination.

There should not be rigid rules governing who is a parent, he said.

Instead, he argued for the application of federal family law, and said the question of who is a parent should be determined by the circumstances of each case, with reference not only to who provided the genetic material but also who had participated in social and psychological parenting of the child.

Mr Masson's position was backed by the Commonwealth attorney-general and the independent children's lawyer.

The term "parent" should take its ordinary and contemporary meaning, they argued.

The two women on the other hand, said the NSW laws applied so as to preclude a sperm donor being a parent.

The women were backed by the intervention of the Victorian Attorney-General, who, though not directly linked to the case, has argued that it is the state law about the status of children born of artificial insemination that applies.

The state says that its approach provides more certainty than the approach of the children's lawyer and the Commonwealth, which treated "the term 'parent' as a question of fact to be resolved on a case by case basis by reference to evidence of intention and/or social parenting".

In written submissions, the state said this would leave uncertainty as to whether a donor is a legal parent at the time of the child's birth, when no social parenting has yet had time to happen, and that it's unclear what level of social parenting would render a sperm donor a legal parent.