Brennan and 37 other republican prisoners broke out of the Maze in 1983
Pól Brennan fled Northern Ireland in 1983 after breaking out of the high security Maze Prison.
He had been serving 16 years after being caught moving explosives and weapons for the IRA in 1977.
Brennan went on the run and entered America on false papers the following year, where he has remained ever since.
At the weekend he returned to Irish soil after being deported.
The jail break was the biggest in the UK's history, with 38 republican prisoners escaping.
A prison officer died of a heart attack after being stabbed while trying to stop some of the men getting away.
Ten were recaptured within a few hours but the remainder went on the run, some later emerging in north America, including Brennan.
Pól Brennan fled Northern Ireland in 1983
In the 1990s he, and other Maze escapers Kevin Artt, James Smyth and Terence Kirby were arrested separately in the US.
Smyth was extradited back to NI in 1996 and returned to prison, before being released in 1998 as part of the Good Friday Agreement.
The FBI arrested Brennan in California, in 1993 after he applied for a passport using an alias. That started a seven-year fight against extradition, during which Brennan spent about four years in US jail.
Requests for his extradition and those of Artt and Kirby by the UK authorities were dropped in 2000 following the outworkings of the Agreement and it seemed as if he was safe in the US.
He had married Joanna Volz, an American citizen, 20 years ago, and had been living in California, working as a carpenter in the San Francisco Bay area.
In January 2008 they drove to Texas where Ms Volz was going to help care for family members when they were stopped at an immigration checkpoint.
Brennan was detained at a checkpoint in Texas
When officials saw his work permit had expired, he had applied for it to be renewed but had not received his new one, they checked his unusual background and detained him based on his criminal history.
He had been convicted of making a fraudulent passport application and using an alias when buying a pistol in his early days in California.
In 2004, he was charged in California State court with assault with a deadly weapon after he caused serious bodily injury by repeatedly striking a man with a cordless-drill battery.
He pleaded guilty to a lesser charge of misdemeanor simple battery, and was sentenced to 30 days in jail, three years conditional probation, 500 hours of community service, a $1,500 fine, and was required to attend anger-management sessions.
At an immigration hearing in November, Brennan asked the judge to consider granting him political asylum due to reprisals he said he could face in Northern Ireland, or permanent residency taking into account his 1989 marriage to Ms Volz.
He had appealed, unsuccessfully, to the head of Homeland Security Janet Napolitano to overturn the decision based on the hardship it would cause his wife.
His supporters have said he is being punished for his political past and Sinn Fein politicians have said he should be allowed to stay in America.
Some unionists, however, have said that he should be returned to prison to finish the sentence interrupted by his 1983 escape.
The DUP's Jeffrey Donaldson said this week that Brennan should be returned to jail.
"He has a remaining sentence to be served for terrorist crimes and he committed another criminal offence whilst escaping from the Maze," he said.
Brennan is now in the Republic of Ireland and has said he will stay for a while, before deciding if he will venture north.
While he officially remains a fugitive, in 2003 the Northern Ireland Prison Service said he, along with Artt and Kirby, were not being "actively pursued".