There are the Iraqi Shi'ite militia who have sworn allegiance to Iran and the politicians beholden to Tehran. There are the Iranian companies that make everything from Baghdad's yellow taxis to the refrigerators and air conditioners that flood street markets.
And then there are the dates.
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Iraq was once the world's biggest producer of the sweet fruit. But decimated by years of neglect and the 1980-88 war with Iran, production has declined to such an extent that imports are now banned to protect the local industry.
That has not stopped smugglers, particularly Iranian producers who hide their dates under cartons of other fruit. Saudi Arabia is also a big producer but the Iranians have cornered the market.
It's a blow to national pride which some Iraqis see as emblematic of Iran's growing hold on their country.
"Haqiqat dates are now the best in Iraq," Mehdi Haqiqat, owner of Iranian firm Haqiqat Golden Dates, said by telephone.
Three years ago, 20 percent of his dates were sold in Iraq, he said. Now that figure has risen to more than 90 percent.
"The government is doing nothing. Iran controls Iraqi politics and the economy," said Qusay Hamdan, a trader at a market outside Baghdad.
Iraq is one of multiple proxy battlefields as Shi'ite Muslim Iran and Sunni Saudi Arabia seek the upper hand in the Middle East.
The regional powerhouses back opposing sides in conflicts in Syria and Yemen. They are also rivals in Lebanon, where Iran exerts influence through the Hezbollah political and military movement which Saudi Arabia considers an enemy.
Their rivalry and the regional conflicts have deepened instability in the Middle East and stoked fears in Western capitals including Washington of a direct confrontation between Riyadh and Tehran that might draw in their international allies.
Although Iran fought a war with Iraq from 1980 to 1988, it has a big head start over Saudi Arabia.
Riyadh and Baghdad began taking steps towards detente only in 2015, after 25 years of troubled relations starting with late dictator Saddam Hussein's invasion of Kuwait in 1990.
Iran has been increasing its influence in Iraq since the U.S.-led invasion that toppled Saddam in 2003, and the countries are now close allies. Tehran cemented ties by helping Baghdad to defeat Islamic State, a mutual enemy, and to stifle a push for independence by its Kurdish population.
The improvement in relations has enabled Iran to forge ties in many areas, including business.
"It's the same ploy. Help the Iraqis, then make sure they help you set up legitimate businesses...," said a Western diplomat who has followed Iran closely for years.
Iran is now Iraq's top trade partner, with annual turnover of about $12 billion, according to an Iraqi officials. Annual trade between Saudi Arabia and Iraq stands at about $6 billion.
Tehran exports foodstuff, livestock, construction material and plastic products to Iraq. Local traders say Iranian food items and inexpensive vehicles, including the yellow taxis that are everywhere in Baghdad, dominate Iraqi markets. Quality is decisive when it comes to dates, according to deputy Agriculture Minister Mahdi al-Qaisi, as are marketing and packaging.
"It's a process that we are still unable to match so far," he told Reuters.
No longer king of dates
Iraqi officials say it is impossible to tell how many foreign dates are sold in Iraq because they are brought in illegally. But it is clear Iraq is no longer the king of dates.
During its heyday, Iraq produced three quarters of the world's dates. It now accounts for about five percent of global output and is only the seventh biggest producer, according to the International Nut and Dried Fruit Council Foundation.
"Iranian dates have the lion's share (of those) being marketed inside Iraq compared to the Saudi, Emirates and Kuwaiti dates because Iran has multiple border crossings with Iraq in Kurdistan and the southern provinces," said Abbas al-Quraishi, who advises Iraq's Union of Farmers' Cooperatives.
Iraqis' liking of Iranian dates was evident at a sprawling market outside Baghdad where traders were busy arranging colourful cartons of them in long rows. Some have given up on local dates because they make big profits selling Iranian ones.
"We don't want the government to end the smuggling. We are selling," said market trader Muhammed Hamid. "Three years ago Iraqi dates sold for 3,000 dinars ($2.5) a kilo. Now they sell for 1,000 because of competition from Iran."
Nearby lay boxes of dates from Saudi Arabia.
Many Iraqi farmers can barely make ends meet. In addition to water shortages and a lack of pesticides, they have to buy gas for generators to keep refrigerators going through Iraq's frequent power cuts, a burden Iranian producers do not face.
"We suffer from losses of up to 70 percent because of Iranian dates," said farmer Adnan Jaber, 58.
Other complain of corruption and bureaucracy. Far removed from regional power struggles, they just want to survive.
"The government gives us water but it’s not enough. The pesticide plane comes once a year," said Maitham Kathim, 35.
A trade ministry spokesmen said Iraq was doing everything in its power to protect local industry, including subsidies for farmers, but that the country had "chosen the path of free markets" since Saddam's fall.
"We want the Iraqi citizen to be able to choose the best product and in some cases the local product is not the best," said Mohammed Hanoun, adding that farmers "need to depend on themselves" and on the private sector.
Starting from behind
Saudi foreign policy has become more assertive since the rise of Crown Prince Mohammed bin Salman, who has said he will protect the kingdom from what he calls Tehran's efforts to dominate the Muslim world.
Riyadh's attempts to increase influence in Iraq are starting to bear fruit. Petrochemical giant Saudi Basic Industries Corp (SABIC) plans to open an office in Iraq and Saudi Arabia’s Industrialization & Energy Services Co (TAQA) is opening an office in Iraq to boost the presence of the Saudiprivate sector in Iraq and expand investment.
The Saudi Agricultural and Livestock Investment Company (SALIC), an arm of the country's Public Investment Fund, is looking at farmland investment opportunities. The two countries are discussing a power-grid link initiative and investments in petrochemicals, renewable energy and power generation projects.
But Riyadh still has a long way to go to catch up with Tehran in Iraq.
Tehran has vast sway over the government, led by fellow Shi'ites, and trains and funds powerful Shi'ite militias. Top Iranian commanders could be seen on Iraqi battlefields giving orders in the war against Islamic State. Iraq and Iran have signed $7 billion in contracts in techno-engineering services, the Iranian news agency IRNA said. Private Iranian investors set up a factory in 2014 which produces about 100 automobiles per day.
Following Iran's help in putting down the Iraqi Kurds' push for independence, Iraq is expected to start supplying crude oil for the first time from the Kirkuk fields in Iraqi Kurdistan to a refinery in the Iranian city of Kermanshah.
An Iraqi oil official said the initial shipments would start soon and would initially be 40,000 barrels per day.