R.K. Ramazani adds value:
Iran’s build up of influence is limited … for two major reasons. First, Iraqi nationalist sentiments place serious limits on the exercise of Iranian power. Even the pro-Iranian political factions are quite sensitive about foreign impingement on Iraqi sovereignty. The fellow Shia Iraqi forces, contrary to Iranian expectations, did not rise up against Saddam Hussein in the Iran-Iraq war; they fought against Iran. The other reason pertains to numerous disputes between the two countries. Many of these have been inherited from the Iraq-Iran war. They range from war reparations to border problems and continental shelf delineation in the Persian Gulf. For example, in 2009 Iranian forces penetrated Iraqi territory, as they had in 1982, and occupied the disputed Fakka oilfield for a few days. A more serious dispute between the two countries concerns Iranian border crossing. Iran repeatedly pursues an Iranian Kurdish separatist group into Iraqi territory.
Fred and Kim Kagan shrilly declare Iranian victory after the withdrawal. Matt Duss is as exasperated as Ted Galen Carpenter:
As for the idea that the U.S. withdrawal will "unquestionably benefit Iran," newsflash: The Iraq war unquestionably benefited Iran. As an Iraqi friend put it to me at a conference in 2008, “America has baked Iraq like a cake, and given it to Iran to eat.” As the New York Times reported earlier this month, Iran’s influence in Iraq — which was always primarily political, not military — has actually declined over the past two years (as with Al Qaeda in Iraq, the U.S. has benefited from our adversaries’ ability to alienate their own allies), but it’s worth noting that Iran’s influence was at its height when there were over 100,000 U.S. troops in Iraq. Does anyone seriously imagine that a few thousand extra U.S. troops would make the difference here?