Nauru won't meet promise on refugee claimsLawyers challenge offshore detention centresNauru rape victim begs to come to Australia for an abortion
Australia does not control the controversial Nauru detention camp and a Bangladeshi mother and baby who are "terrified" of being returned there would be free to come and go, the High Court has heard.
The assertion was made by lawyers for the Commonwealth on the second day of the challenge to the lawfulness of Australian-funded detention centres at Nauru and Manus Island, which argues the federal government does not have the power under the constitution to detain people overseas. 
The test case has wide implications for Australia's offshore processing regime and, in particular, about 200 people who have been detained offshore and are now in Australia temporarily, including more than 50 children and victims of violence and sexual assault.
The plaintiff is a woman from Bangladesh who was brought to Australia from Nauru in   August last year for medical treatment. Her daughter is now 10 months old and supporters say the mother is "terrified" of returning to Nauru.
Australia's involvement in the centre is a key point in establishing if the federal government is operating outside its powers.
Counsel for the Commonwealth Justin Gleeson SC told the court on Thursday that the centre operates at the will of the Nauruan government and Australia helps the republic to "carry out its law on its soil".
He rejected suggestions made by the woman's lawyers on Wednesday that a Nauruan operations manager was involved only at the "helicopter level" at the centre, saying the official was responsible for its day-to-day running.
"Large or small, everything traces back to the operations manger," Mr Gleeson said.
Australia funds the centre and contracts Transfield Services and Wilson Security to operate and secure it, but those firms played only a support role, Mr Gleeson said, adding the Australian contractors "cannot be subject to direction by an officer of the Commonwealth".
While the federal government applies and pays for visas that required people to be detained in the centre, Nauru is a sovereign state that "determined whether any person ??? enters Nauru", Mr Gleeson told the court.
"Nauru determines whether to accept [them] and critically Nauru determines the conditions of the visa," he said, adding Nauruan law also decided who was allowed to leave the centre, and under what conditions.
The woman's lawyer Ron Merkel QC told the court on Wednesday that, through a contract with Transfield Services, the Commonwealth funds, controls and implements the powers of detention.
Federal government actions such as asking Nauru to establish the camp, procuring a perimeter fence to keep people inside and applying and paying for visas that require people to be detained showed the camp was an Australian venture, he said.
The Nauru government this week announced the detention camp would become an "open centre" 24 hours a day, and detainees would be free to come and go as they pleased.
On Thursday Mr Gleeson told the court this meant the detainees are no longer required to remain inside the detention centre, but may simply use it as a place of residence. The woman's lawyers have contended this arrangement could be revoked at any time.
The woman's lawyers also argued that the federal government's contact with Transfield Services was invalid. Stephen Donaghue QC, acting for Transfield Services, rejected this and said the contract "follows the detention rather than causes it".
The court reserved its decision.
Follow us on Twitter