Analysts say concerns in Gulf Arab capitals and some Iraqi quarters that Tehran will fill any post-American vacuum are greatly exaggerated, even if Iran is the foreign power with most influence in Baghdad
Tehran bids to boost its influence
Iran will strive to bolster its influence in Iraq now American troops have withdrawn, hoping that Baghdad can replace Syria as a key ally in an unfriendly Arab world if President Bashar Al Assad is deposed.
The US pull-out has left behind an Iraqi government dominated by Shiite parties beholden to Iran, which sheltered some of them for years when Saddam Hussein's minority Sunni regime was in power.
Iranian diplomacy in Baghdad will be very active and Tehran is also likely to step up infiltration of Iraqi intelligence services.
But analysts say concerns in Gulf Arab capitals and some Iraqi quarters that Tehran will fill any post-American vacuum are greatly exaggerated, even if Iran is the foreign power with most influence in Baghdad.
Those fears ignore the depth of Iraqi and Arab nationalism. The US could not dominate Iraq when it had 170,000 boots on the ground, and Iran cannot expect to fare any better if it tries to follow suit.
"I don't think Iraq will ever be dependent on Iran - it's simply too big, rich and powerful," said Sir Richard Dalton, a British former ambassador to Tehran.
Joost Hiltermann, an Iraq expert at the International Crisis Group, agreed. "Very few [Iraqis] support Iran's system of religious rule and, basically, they don't trust the Persians," he said in an interview from Washington. "I don't see Iran having a lot of purchase in Iraq, even with the Shiites there."
Nouri Al Maliki, Iraq's Shiite prime minister, has nurtured good relations with Tehran, but is by no means an Iranian puppet, analysts say.
"Certainly Iran is going to get a sympathetic hearing in Iraq … but the Iraqis are not in the least interested in having Iranian tutelage," said Gary Sick, an Iran specialist at Columbia University in New York. "If Iran tries to push things in that direction, Iraq is going to push back."
Nor can Iraq reprise Syria's strategic role for Iran because it does not have borders with Lebanon or Israel. Damascus, Tehran's main Arab ally during the past three decades, helped channel Iranian arms to Hizbollah.
Without Syria, Iran would also lose its conduit to Hamas, which is headquartered in Damascus.
Even so, Iraq can serve as a valuable friend for Shiite Iran in a largely hostile Sunni Arab world, provided Tehran does not overplay its hand.
The sectarian crisis that has erupted in Iraq after the American pull-out will be a key test.
Tehran had pushed for the Americans to leave, viewing their long presence on its western flank as a constant threat.
But, despite suspicions among Iraqi Sunnis and Gulf Arab countries that Tehran is stoking the combustible Iraqi pot, Iran has reason to view the crisis with unease and may well try to restrain Mr Al Maliki, experts said.
The 2003 US invasion of Iraq was a huge strategic gain for Tehran, removing its most dangerous enemy, Saddam Hussein, without Iran lifting a finger.
That fortuitous prize could be endangered if the Iran-friendly political order in Iraq descends into sectarian bloodletting which could see Saudi Arabia, Iran's main regional rival, increasing its support for Iraq's Sunnis.
Iran also faces strong competition for influence in Iraq from Turkey. And Baghdad will want to maintain good relations with the US: Mr Al Maliki this week invited American firms to help rebuild Iraq.
Iran's friendly relationship with Iraq faces other stiff challenges in the future.
"If the conflicted Iraqi leadership can get their act together, the historical strategic rivalry between Iraq and Iran is bound to re-emerge in the longer term, particularly when Iraq begins to surpass Iran as an oil exporter," said Farideh Farhi, an Iran expert at the University of Hawaii.
For Mr Sick, a "key test" will come when Iraq and Iran attempt to resolve long-standing border issues, which both appear keen to postpone for now.
A historic dispute over control of the strategic Shatt al-Arab waterway, known in Iran as the Arvand Rud, helped trigger the eight-year Iran-Iraq war in the 1980s.
For many observers, Tehran's decision last month to install a top Iranian cleric, Ayatollah Mahmoud Hashemi Shahroudi, in the Iraqi holy city of Najaf, the spiritual capital of Shiism, signalled Iran's determination to increase its leverage in Iraq.
Iran's intention seemingly was to undermine Iraq's most revered Shiite cleric, Grand Ayatollah Ali Sistani. He is a force for moderation who favours a "quietest" tradition under which clerics advise rather than actively participate in politics, although he has been strongly critical of Mr Maliki's government.
The cornerstone of Iran's theocratic system, in contrast, is the supremacy of clerical rule over temporal and spiritual affairs, known as velayat-e-faqih. It holds little attraction for Iraq's Shiites.
Ayatollah Shahroudi is tainted in Iraqi eyes by his closeness to Iran's supreme leader, Ayatollah Ali Khamenei. He also headed Iran's hardline judiciary during the brutal crackdown on mass protests that erupted after President Mahmoud Ahmadinejad's "stolen" re-election in 2009.
Despite trying, Iran accepts it cannot position one of its own ayatollahs to succeed the octogenarian Mr Sistani, said Sadeq Saba, the head of the BBC's Persian Service.
Iran, he added in an interview, has "learned to be pragmatic in its foreign policy".
Tehran will, however, rely on Mr Shahroudi to serve as an "intellectual asset" in Najaf, ensuring that Iraq's Shiite clergy does not become overwhelmingly opposed to Iran's velayat-e-faqih system, said Trita Parsi, president of the National Iranian American Council.
That Iran has legitimate interests in Iraq is often overlooked. Thousands of Iranian pilgrims visit Najaf daily and the two countries, which share a long border and historical ties, have a mutual interest in being on good terms.
Memories are fresh of the devastating Iran-Iraq war, which killed nearly 400,000 people.
"The overarching interest of the Iranians is that there is never a repeat of that war … this means ensuring that Iraq never serves as a proxy or puppet of a hostile foreign power," said Mr Parsi. "Both sides have paid the price of conflict and they don't want it again."
For Ms Farhi, "the claim of Iran's undue influence in Iraq is without a doubt overstated".
"Given Iraq's raucous politics, it is hard to imagine any country controlling Iraq," she added.