The family at the heart of the "Home To Bilo" campaign will remain in Australia for at least another 24 hours as a legal argument about the immigration assessment of two-year-old Tharnicaa continues.

Key points: The Federal Court extended an order preventing the deportation of the Tamil family to Sri Lanka until 4:00pm tomorrow

The Federal Court extended an order preventing the deportation of the Tamil family to Sri Lanka until 4:00pm tomorrow Government lawyers argued that the girl's detention was valid and that her application was handled appropriately

Government lawyers argued that the girl's detention was valid and that her application was handled appropriately The family's lawyers argued that for a period of time in 2017, the case of her mother Priya had not been "finally determined" and therefore Tharnicaa's case was not settled

The Tamil family Nadesalingam Murugappan, known as Nades, and Kokilapathmapriya Nadesalingam, known as Priya, and their Australian-born daughters Kopika, aged four, and Tharnicaa, aged two, have fought and lost numerous court battles to remain in Australia.

The family has been in limbo since March 2018 when they were taken away from their home in the central Queensland town of Biloela, which has lobbied hard to keep the family in Australia.

On Wednesday, lawyers for Tharnicaa argued that for a period of time in July and August 2017, the case of her mother Priya had not been "finally determined" and therefore Tharnicaa's case was not settled.

They argued that for that period of time in 2017, Peter Dutton, then-immigration minister, had "lifted the bar" for visa applications, therefore removing the restrictions to apply.

In May of that year, the Federal Government announced that asylum seekers had until October 2017 to apply for a visa or be returned to their home countries.

The daughters Tharnicca (left) and Kopika (right). ( Supplied: Tamil Refugee Council )

Lawyers of family question assessment process

Yet the toddler, who was born in June 2017, was not given the opportunity to apply, the court heard.

Priya's case was finalised in late August 2017.

Tharnicaa's lawyers also argued that the "statutory process" of assessing her visa was "still in train" because she had been detained for that purpose.

Further, they argued that if the Government claimed it was not assessing her and not still undertaking a "statutory process", then her detention was not valid.

The court heard barrister Angel Aleksov question whether his client was lawfully detained.

"If she's removed from Australia she will have no right to re-enter," he told the court.

"The ultimate claim is her right to seek a visa."

Government lawyers argued that the girl's detention was valid and that her application was handled appropriately.

During the hearing, Judge Mordecai Bromberg clarified that the family's lawyers were essentially arguing the Government had not been "compliant with Australian law and the rules of procedural fairness".

The Federal Court has extended an order preventing the deportation of the Tamil family to Sri Lanka until 4:00pm on Thursday.

There was detailed argument about the wording of several sections of the Immigration Act as well as the numerous policy changes that have been enacted by the Federal Government.

The family has been on remote Christmas Island since late August after lawyers were successful in getting an injunction preventing their deportation to Sri Lanka based on claims Tharnicaa's case needed to be independently assessed.

The Government has responded since telling the court two weeks ago the toddler had been assessed and would not be granted a discretionary protection visa by the Immigration Minister David Coleman.

Lawyers for the family have questioned the assessment process, which happened quickly and on the same day citizenship was sought for the child.

Judge Bromberg will make a decision on Thursday about whether the case will go to a full hearing at a later date.