By Jonathan Head
BBC News, Istanbul
It is one of the abiding images of the last century.
Late in the afternoon of 13 May 1981, the most charismatic pope of modern times was touring St Peter's Square in his Popemobile before giving his weekly address.
In those days, it was an open-top vehicle offering little protection. But at the time, few thought any protection was needed.
Pope John Paul II was reaching out to the crowd, picking up small children and kissing them.
Agca's motive for shooting the Pope remains a mystery
Several shots rang out. The Pope stood, looking stunned, for a moment, then collapsed into the arms of his personal secretary, blood seeping from his abdomen.
He was rushed to hospital, where, after five hours of surgery and losing three quarters of his blood, he narrowly survived.
A photograph captured the moment, a hand holding a gun seen clearly pointing out from the crowd. The would-be assassin was quickly caught at the scene. He was a young, good-looking Turkish man named Mehmet Ali Agca.
Twenty-nine years later, a now grey-haired Agca was driven away from the high-security prison outside Ankara where he has spent the past four years.
Aside from some military bureaucracy - he is still technically liable for Turkish military service - he is a free man. But his motive for shooting the Pope remains a mystery.
Initial investigations by the Italian police revealed he was a member of an ultra-nationalist group, the Grey Wolves, which was involved in a violent confrontation in Turkey with leftist groups in the late 1970s, which left thousands dead.
MEHMET ALI AGCA
Escaped from Turkish prison while awaiting trial for murder of newspaper editor in 1979
In July 1981, sentenced to life imprisonment in Italy for attempting to kill Pope John Paul
Pardoned at Pope's request in June 2000, extradited to Turkey
Convicted for murder, robberies and prison escape, served time in Turkish jail
Released on parole in January 2006
Ruled "unfit for military service" because of "advanced anti-social personality disorder"
Returned to jail after eight days after court ruled jail term miscalculated
He had escaped from prison in Istanbul in November 1979 while on trial for the murder of a liberal newspaper editor, and was later sentenced to death in absentia.
He had wandered through several European countries before arriving in Italy three days before the shooting.
But that is where the facts run dry, and the conspiracy theories begin.
Under questioning, he, at first, said he was linked to a militant Palestinian group. Later, he blamed the Bulgarian secret service and the Soviet KGB for organising the assassination attempt.
It was a plausible enough hypothesis. Pope John Paul was an outspoken opponent of communism, and had become an inspiration to the dissident Solidarity movement in his native Poland.
This led to the prosecution of three Bulgarians and four Turkish nationals.
But Agca's increasingly wild testimony, in which he claimed to be a reincarnation of Jesus Christ, undermined the case, and all the defendants were acquitted in 1986.
He was sentenced to life imprisonment in 1981.
The Pope was quick to forgive his assailant, visiting him in prison in 1983 and talking to him for 20 minutes. But he insisted their conversation would remain secret.
The Pope later described Agca as a trained assassin who could not have been acting alone; but he also believed that both the attempt on his life and his survival were due to divine intervention.
He donated the bullet recovered from his abdomen to the shrine in Fatima, Portugal, where he believed the shooting had been foretold by the Virgin Mary to three local children in 1917.
Agca had also referred to that prophesy during his trial.
The Pope's intervention led to Agca being pardoned in 2000, and sent back to Turkey, where his death sentence had been commuted to 10 years in prison.
He served the rest of the sentence, despite a moment of confusion in 2006 when he was briefly released, and then imprisoned again on the orders of the Turkish Supreme Court.
He has continued to issue outlandish statements right up to his release, claiming to be a new messiah and predicting the end of the world.
So is he delusional? Not according to those who have spent any time with him. Journalist Mehmet Ali Birand met him three times in his Italian jail cell.
"He's a balanced guy, he was in control of the situation, in control of himself, but full of conspiracy theories.
"The impression I got was he was doing this deliberately. He liked playing with the media. He wants to cash in - he believes that if it had not been the Pope, he would not have stayed in prison so long."
Cashing in is certainly a possibility. Agca's lawyers say he has been offered up to $3m (2.1m euros, £1.8m) by publishers for exclusive rights to his story. But it is still unclear whether that story will have any credibility.
The other mystery surrounds his Turkish connections.
The Grey Wolves group, with which he was associated at the time of the shooting, was linked to an underground network known as Gladio.
This was set up with CIA support in a number of European countries during the Cold War to prepare resistance to a possible Soviet invasion.
In both Italy and Turkey, Gladio networks are believed to have been behind numerous bombings and assassinations.
In Italy, the networks have been exposed and dismantled; in Turkey, they are still widely believed to exist as a so-called "deep state", with support from elements of the military.
There are ongoing trials of dozens of people accused of involvement in illegal, deep-state activities.
Agca was certainly helped to escape from prison in 1979 by his guards and some well-known underground right-wing figures. He was given false passports and enough funds to enable him to travel around Europe for several months before the attempted assassination.
The period of Turkey's history just prior to the 1980 military coup is still shrouded in confusion. At the time, the country was in chaos. Groups, both left and right, fought each other, with the alleged involvement of mafia groups and the security forces.
This, together with the many bizarre claims made by Agca, mean his real story will probably never be known. For a man who may still have many dangerous enemies, that could be his best protection.