The detained Biloela Tamil family will today learn if their latest bid to stay in Australia has succeeded

A Tamil family fighting to return home to Biloela in Queensland is expected to learn the outcome of their latest court case.

The Murugappan family marking Nades' birthday on Christmas Island in December 2019. Source: Supplied

For nearly three years a Tamil family who call the Queensland town of Biloela home have fought to be able to return to their community.

Priya and Nades Murugappan and their Australian-born daughters Kopika and Tharunicaa, aged five and three, have been in detention on Christmas Island since August 2019 after an urgent injunction put a hold on their deportation.

On Tuesday morning the family will learn if their latest, and possibly final, bid to return home has succeeded.

Justice Mark Moshinsky had ruled that Tharunicaa was denied procedural fairness in making a protection visa application, which would have allowed her to remain in Australia.

He ordered their costs of $206,934.33 be paid, after determining that Immigration Minister David Coleman had lifted a bar to consider a visa application.

The family, from Biloela in Queensland, were taken into detention in Melbourne in March 2018 and transferred to Christmas Island in August 2019 after an urgent injunction prevented their deportation to Sri Lanka mid-flight.

Supporters of the Biloela Tamil family gather outside the Federal Court in Melbourne. Source: AAP

The federal government appealed Justice Moshinsky's findings from earlier this year, while the family's lawyers filed a cross-appeal against a second ground which was dismissed in that case.

An appeal hearing was expected to run over two days in October last year, but took significantly less time after Justice Geoffrey Flick, one of three hearing the case, became "cranky" at the government's barrister for repeating himself.

Each of the hearings has prompted a gathering of the family's supporters outside court, singing the children's favourite songs.

Victoria's lockdown means that won't be allowed on Tuesday.

As well as the federal government's appeal a decision will also be handed down in a cross-appeal filed by the family's lawyers on a second ground for relief which was dismissed in the first Federal Court hearing.

There is no automatic right of appeal to the High Court from the full bench of the Federal Court.

That means if either party wishes to appeal the case further they must first seek special leave from the High Court.