The woman, aged 48, who was identified by the pseudonym "Betty Colt" during court proceedings in the Southern Highlands, is being held in Villawood detention centre after being released from jail in August after serving nine months for attempting to kidnap her children from foster carers.

Her deportation is said to be imminent.

But the case will be controversial as Colt came to Australia as a child, probably in the 1970s, has lived most of her life here, and has multiple children, some under the age of 16, living in Australia.

The plans for the deportation follow Prime Minister Malcolm Turnbull's visit to New Zealand last week in which he took a tough stand with the New Zealand government on Australia's right to deport convicted criminals.

The case of the Colt family horrified Australians and drew global interest when the Herald first revealed it in 2013. 

The Children's Court proceedings revealed that Colt was the matriarch of a family of 40 discovered living on a property outside Canberra in mid-2012 in squalid conditions, without running water and electricity, in ramshackle caravans, sheds and tents.

Twelve children under 18 were removed, and subsequent genetic testing revealed that several were the progeny of brothers and sisters, fathers and daughters, or uncles and nieces. 

Once in care they told carers of horrific sexual abuse by adults and by siblings on the isolated farms, on children as young as 12.

They were undernourished, had developmental delays, poor dental and general hygiene and had barely attended school.

In ordering the children to be removed to care, Judge Peter Johnstone, president of the Children's Court, noted: "Betty Colt's children, Bobby, Billy, Brian, Dwayne and Carmen [also pseudonyms] exhibited features indicative of neglect when they were taken into care.

"They were lacking basic life skills, such as the ability to shower and clean their teeth voluntarily.

"Their living environment was inadequate and their health and dental needs had been severely neglected.

"Additionally, their schooling and educational needs had been ignored, contributing to their developmental delay and deficits in intellectual functioning."

Subsequent genetic testing found they had parents who were related, though the incest was denied by Colt and other adults.

The judge concluded that "Betty Colt's ability to function as an effective parent was impaired by her enmeshment in a dysfunctional intra-familial structure" and ordered her five children under 16 to be placed in foster care.

But in making the orders, the judge also noted that this appeared to be a case of intergenerational incest and that Colt may well have been a victim of incest herself, with the possibility that her own father was the father of one or more of her children.

Two of Colt's sons, aged 13 and 15, were placed with families and sent to school but Colt struggled to accept their removal.

In 2013, she hatched a plot to snatch them back from their carers and smuggled them a mobile phone which she had used to contact them and make arrangements for them to abscond. The police were listening to her calls and intercepted the plot.

In November 2014, she was found guilty of two charges of procuring the removal of a child from care and one charge of recruiting her older child to carry out or assist in criminal activity, being the kidnapping of the younger child.

She was sentenced to one year in jail.

Despite the genetic evidence and extensive efforts by the child sex abuse squad of the NSW Police, none of the family has been charged with any incest-related charges.

It is unknown whether Colt has any relatives remaining in New Zealand. However, her high-profile case is likely to fuel debate about the ethics of deporting New Zealanders with long-standing and entrenched ties to Australia.

Comment has been sought from Immigration Minister Peter Dutton and from the New Zealand High Commission.