Akeli Lane has always said she gave her two-day-old baby Tegan to the infant's biological father.
But as part of an appeal against the 38-year-old's murder conviction, her legal team says the option of manslaughter should have been open to the jury.
Akeli Lane, whose once bleached-blonde hair is now brown, displayed little emotion during the one-day hearing at the NSW Court of Criminal Appeal on Tuesday.
Dressed in a pink and black blouse, the former waterpolo player and teacher gestured from the dock to her long-term boyfriend Patrick Cogan, her mother Sandra Lane and her father, retired policeman Robert Lane.
Among the reporters and court enthusiasts who also filled the gallery was Department of Community Services (DoCS) worker John Borovnik who first flagged Tegan's disappearance with an adoption agency in 1999.
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The crown says that three years earlier - on September 14, 1996 - Lane killed Tegan after leaving Auburn Hospital with the newborn.
She then went to her parents' home before attending a wedding later that afternoon.
Lane, by contrast, has always maintained she gave Tegan to the infant's father, with whom she had a brief affair and who she said was called Andrew Norris or Morris.
Police investigations have failed to uncover either the father or the daughter.
She is now appealing her conviction on eight grounds, including that an alternative count of manslaughter should have been open to the jury.
In arguing the case, barrister Winston Terracini SC said the crown could not prove how Tegan died or that Lane had any intention to kill the newborn.
"She (Tegan) could have been placed in a bag ... and died as a result of gross negligence," he submitted.
"There are a whole range of incidents that end in an unlawful killing but fall short of an intention to kill."
But Justice Carolyn Simpson observed that Lane had had two terminations as a teenager and kept three pregnancies and births secret from family and friends.
Tegan was the middle child of the three secret babies, with the other two infants adopted out.
"You couldn't draw an inference of manslaughter from a history of determinations not to keep a child," she said.
Acting for the crown Jennie Girdham SC said the defence case throughout the trial was always "murder or nothing" and that the appeal ground meant Lane's case had "taken on a new complexion".
While she accepted that the crown's case was highly circumstantial, she says when the evidence was taken as a whole the jury came to the conclusion that Lane killed Tegan and did so with "murderous intent".
If Lane had hypothetically left the child to die somewhere, she argued this would also be akin to murder.
Chief Justice Tim Bathurst, Justice Simpson and Justice Christine Adamson have reserved their decision on the appeal.
Lane was sentenced to a minimum of 13 years and five months and a maximum of 18 for Tegan's murder.
If her appeal is unsuccessful her earliest release date is in May 2024.
