Officially, the government does not recognize any of these armed groups. As a practical matter, many of these gangs are protected by one senior government official or another. Religion, as always, is a popular screen for politicians to hide behind. Say the right things, back the right people, and you can get away with murder. More importantly, you can get away with the most outrageous bits of corruption.
Unofficially, the government is under tremendous pressure by the United States to shut down the militias. Especially in light of the chaos among the Palestinians and Lebanese, because of private armies. The government encourages shutting down the private armies that support Sunni Arab terrorism. That includes al Qaeda, which operates under the protection of several religious or tribal warlords.
Although Iraqis were able to elect national leaders and legislators, democracy has not worked so well at the local level. Guns outweigh votes. So when the American show up to do some gang-busting, the cell phones go to work. The Americans have their own tip lines, and have intel operators who are good at evaluating the tips that come in. The number of raids that have nailed nests of bad guys, or captured large arsenals of weapons, has increased over the Summer.
Cell phones have made it much safer to turn in terrorists, or just local thugs. In some areas, the gunmen try to ban the use of cell phones. But that is difficult to do unless you are willing to go without them yourself. For the only way to be sure that the cell phones are off is to take down the cell phone antennas in an area. Some gangs are desperate enough to do this, relaying on a small number of satellite phones to keep in touch.
Cell phones continue to be the terrorists worst enemy. In western Iraq (Anbar province), and parts of Baghdad dominated by Islamic fundamentalist religious militias, cell phones have become increasingly important tools in fighting the bad guys. It seems that many Iraqis living in these areas are not happy with the way their local Islamic fanatics are running things. For example, if you do not look "Islamic enough," the local Islamic enforcers can kill, mutilate or humiliate you. These guys see someone wearing jeans (which are considered decadent Infidel custom), and they kill you. Wear shorts to work, and the local enforcers of Islamic correctness may shoot you in the bare legs. Women showing too much (hair or skin) can be beaten, stripped naked or have their head shaved. Any kin of the women trying to intervene can be beaten, or shot. Women are also attacked if they are caught using a cell phone in public. Actually, some men have been shot at for using a cell phone, because the bad guys have figured out that cell phones have been used to let the Americans or Iraqi troops know where the local thugs are living, storing their weapons, or traveling on their way to plant a bomb or shoot at convoys.