Looking at the current situation in Iraq, my view is America is regaining Iraq. To a large extent, from an Iraq that looked very much in the hands of Iran, to a federal Iraq that requires American presence to keep its three primary components together and help provide the needed, internal security and preserve its boundaries. Reluctant as the pro Iran south is, they have or will very soon realize that they will lose the country without the help of USA/GCC Coalition. Iran alone cannot provide the resources to stop ISIS (the battle from the sky is a USA led global coalition), the Sunnis will only collaborate with American and GCC support and guarantees and the Kurdish North has existed only with American help. The American army will most likely maintain bases in the north and centre of Iraq and the new Iraq will need America to maintain its integrity, internal and external security and this is becoming clearer by the day.
Iran is stretched to the limits of its military and financial resources in regional conflicts, has its own problems internally and with the global community and a very troubled economy. Not that Iran will lose all, it will have friends and allies in Iraq but like Lebanon it will have influence but not the country.
Looking further down the road, I don't see Iran achieving any meaningful gains regionally. For a nation or a regional power can only sustain its role or expand it with an expanding sustainable economy that is growing faster than its other regional competitors, to support and finance such an expansion.
I see weak oil for years to come. Iraq, Yemen and Syria as financial liabilities and a very badly managed, very wasteful Iranian economy. An economy that is losing economic market share of the total regional GDP against much better managed GCC and Turkish economies.