The disappearance of Saddam Hussein and his top aides has sparked contradictory rumours about their fate - are they dead, alive and still in Iraq or have they fled the country?
Some Baghdad residents are convinced that the Iraqi leaders survived US efforts to kill them.
The BBC's Middle East analyst, Roger Hardy, says many experts also think that Saddam Hussein is still in Iraq - and that is the view of senior British officials.
The Americans twice bombed buildings in Baghdad where they thought the Iraqi leader was hiding - on the first day of the war, and then again on 7 April when they targeted a restaurant in the suburb of Mansour.
The Mansour raid left a huge crater - but was Saddam Hussein there?
The residents of an area in northern Baghdad - around the Adhamiya mosque - say Saddam Hussein appeared there two days after the Mansour raid.
They told a correspondent for the New York Times that Saddam Hussein delivered a tearful but defiant farewell message, outside the mosque.
By the time US troops - and a BBC correspondent - arrived at the mosque some hours later, they say, Saddam and his younger son Qusay had already made their escape.
'Fighting in the same trenches'
According to one man, Saddam Hussein and his entourage turned up in three cars. The embattled Iraqi leader then stood on one of the cars to address the crowd.
"I am fighting alongside you in the same trenches," the man quoted the Iraqi president as saying.
The Adhamiya area has long been a stronghold of Saddam Hussein's Baath Party, the New York Times reports.
The BBC's Roger Hardy says it is believed Iraqi officials had laid careful plans for the top leadership to be dispersed to different locations inside the country.
When Saddam Hussein told several foreign visitors that he had been born in Iraq and would die in Iraq, he probably meant it, Hardy says.
Rumours abound that the ousted Iraqi leader fled abroad, perhaps to Syria, perhaps with the help of Russian diplomats.
On Sunday, a half-brother of the ousted leader, Watban Ibrahim Hasan al-Tikriti, was picked up by US forces near the Syrian border.
US troops are now scouring Iraq for the missing leader - the Ace of Spades in a pack of cards issued to help the military identify fugitive Iraqi leaders.
The US military has announced rewards of up to $200,000 for information leading to Iraqi regime leaders.
The US operational commander, General Tommy Franks, insists that he has a sample of Saddam Hussein's DNA.
Search in Saddam's birthplace Owja - still no trace of him
And US Brigadier-General Vincent Brooks said on Monday that US experts were carrying out forensic examinations at "a variety of sites".
In the Arab world conspiracy theories about the collapse of the Iraqi regime are rife.
Some commentators view with suspicion the relatively light resistance encountered by US forces when they entered Baghdad.
Abd al-Aziz Salamah, the former deputy head of the Egyptian Intelligence Service, speculates about a possible deal that allowed Saddam Hussein to leave Baghdad in return for Iraqi forces giving up the fight.
But "informed sources" quoted by the Jordanian paper al-Dustur said a senior Republican Guard commander and two other dissident military commanders helped the US forces to target the Iraqi leadership.
After the Mansour bombing a few US tanks ventured into central Baghdad to "test the implementation of the plan to liquidate the Iraqi leadership", the sources said. Finding little resistance, the main US force then poured in.
The sources claim that all the senior Iraqi leaders were killed in the air raid, apart from Information Minister Mohammed Saeed al-Sahhaf and Vice-President Izzat Ibrahim.
Soon after the Mansour raid, US Government officials were quoted as saying there were indications that Saddam Hussein had been killed.
But Britain's intelligence agency, MI6, reportedly told the CIA that the Iraqi leader had left the building moments before the air strike.
American officials are playing down speculation about his disappearance saying that, since his regime is history, his fate is irrelevant.