However, the girl's biological mother Susan and her wife have decided they wanted to move to New Zealand, which triggered Robert to launch a bid to stop them from leaving by proving he is legally the girl's parent as well.
Robert revealed he has been involved in the girl's life for 12 years and has had a big role in her upbringing which included overnight visits, attending countless ballet rehearsals and fostering a close relationship between the girl and his mother. The girl has also been involved with his extended family.
Documents in court reveal Susan has had a second child who is not related to Robert, however submissions claim had has been involved in both the girl's lives, with the second child recently finding out that he was not her biological father, ABC reports.
Robert's lawyers explained that both girls referred to him as "daddy", and he was listed as the first girl's father on her birth certificate.
After an initial Family Court ruling, Susan and Margaret were prevented from moving to New Zealand with the two girls as the women could not prove they were in a de facto relationship.
The conditions of the ruling included that the two women were to be given equal parental responsibility, but that they must consult the man about long-term decisions.
In making her decision, Family Court Justice Margaret Cleary acknowledged the dispute was causing tensions between everyone.
"There is interpersonal bitterness, there are accusations by the two women of manipulative, overbearing conduct by [Robert] and accusations by [Robert] of ruthless exclusion by the two women," she said.
"However, where there is a challenge to a biological parent being a legal parent, as there is here, biology is a part of the answer."
Justice Cleary ultimately found the man was a parent, because he took part in the artificial insemination in the belief he would have a role in the girl's life.
However, the decision was overturned by an appeal to the Family Court, partly based on a New South Wales law governing fertilisation procedures, specifically providing for same-sex couples.
The women successfully argued at the time that Robert, as a sperm donor, could only be legally the girl's parent if he had been married to Susan at the time of conception.
The Federal Government has intervened to support the man, saying he was legally the child's father under the Family Law Act.
The High Court began hearing arguments yesterday and the hearing continues.