The couple took care of the child from the moment she was born, but now have to give her back.

A baby girl relinquished by her mother at birth into the care of a lesbian couple will be "transitioned" back to her biological family after the mother later "changed her mind".

The unusual case in Australia highlights the complexities surrounding "quasi-adoption" and the power of courts to overrule agreements made between friends when one party is struggling with infertility.

The girl, who is now almost three, will be gradually returned to the care of her biological mother and father, with a court finding it in her long-term interest to live with her parents and half-siblings.

During her pregnancy, the girl's mother, known for legal reasons as Ms Grady, agreed to give her newborn to the same-sex couple, known as Ms Blaze and Ms Darnley.

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The couple, who have been unable to have children of their own, took care of the child from the moment she was born.

The couple lived with Grady during her pregnancy and helped run the household.

In a parenting plan drawn up by a lawyer, referred to in court as a "quasi-adoption", Grady requested that she and her three other children have "some ongoing relationship" with the child, although no details were specified.

All three women are profoundly deaf and communicate using Auslan sign language. The father is profoundly deaf, but can communicate using verbal English. The child and her half-siblings have no hearing problems.

During a hearing in the Family Court in October, Grady said at the time she was pregnant, she was struggling financially and believed the child's putative father would not provide any financial support.

Her long-time friends Blaze and Darnley had failed to start a family of their own through IVF, surrogacy or adoption.

Grady thought it important her daughter be bought up by someone with the same disability as her, rather than place her for formal adoption through an agency.

However, two or three months after the baby was born in June 2013, Grady discovered another man was in fact the biological father. After a DNA test confirmed this, the man, known as Mr Harper, said he wanted a relationship with his daughter and would give financial support.

During a visit by Blaze and Darnley and the baby in October 2013, Grady changed her mind and decided she wanted her daughter back. Harper supported her.

On a subsequent visit six months later, Grady "reclaimed" the child, forcing Blaze and Darnley to get the authorities involved. In an interim judgment the Federal Circuit Court ordered the girl live primarily with the couple.

Giving evidence in the trial proper, the couple questioned Grady's parenting skills and her motivation for seeking the return of her daughter. They also mobilised some members of the deaf community to support their "cause" and Grady has been criticised on social media.

Blaze told the court she was worried Grady might "change her mind again".

In a judgment published this month, Justice Michael Kent said it was in the child's best interest to have meaningful relationships with both Blaze and Darnley, as well as her biological parents. But he ruled the toddler live primarily with her parents and set out a four-step transition schedule.

In particular, he relied on expert evidence about the importance of a child's relationship with their biological family and the issues often experienced by adopted children such as questions of identity and rejection. He accepted the expert evidence that it is inevitable the child will "gravitate to her biological family" and grow to resent her adoptive carers.

He also ordered the girl's surname to be changed from Blaze-Darnley to Grady-Harper, although her Christian name will remain the same.

As part of the transition process, the girl will spend one weekend a month with Blaze and Darnley, however they will have no legal parental responsibility for her.