EAJA fees available in immigration habeas petitions & petitions for review
The Second Circuit ruled on April 18, 2005 in Vacchio v. Ashcroft that Equal Access to Justice Act fees are available in immigration habeas petitions.
To require the government to pay your attorney's fees, you must show that you filed a civil action and you were the prevailing party. You will not be paid, though, if the government can prove that its position was substantially justified.
Regarding only the first requirement, the Second Circuit made a new ruling that an immigration habeas corpus petition is a civil action for the purpose of EAJA and therefore can be eligible for the award of attorney's fees. The government (DHS or ICE) had argued that it was not a civil action, but the Second Circuit rejected the government's position.
By the way, the immigrant's attorneys lost their EAJA request because they did show that the immigration habeas was a civil action and that they were the prevailing party by getting the immigrant out of detention, but the Second Circuit (in a split 2-1 decision) ruled that the government's position was substantially justified, for complicated reasons that I won't get into here.
Addition: Using the same logic, the Ninth Circuit also held in November 2005 that a victory in a petition for review to the circuit court can also qualify for EAJA fees. Obtaining a remand back to the BIA is a victory. And when the circuit court's decision concluded that the government's challenged ruling lacked a substantial basis, it was clear that the government could not avoid EAJA fees by arguing that its position was substantially justified. The Ninth Circuit refused to award enhanced fee rates and at the statutory rate ($144/hour in 2002 and $152/hour in 2004), the 64 hours of work were compensated at $9,600 plus $408 in costs. See Thangaraja v. Gonzales, No. 02-73970 (9th Cir. Nov. 3, 2005).
The Ninth Circuit explained why obtaining a remand to the BIA is a victory in Rueda Menicucci v. INS, No. 95-70281 (9th Cir. Dec. 22, 1997) (awarding around $10,000 for 77 hours at $129 per hour); Gwaduri v. INS, No. 02-70629 (9th Cir. Mar. 18, 2004) (awarding $6,750).
Looks like petitions for review often take 65-85 hours of work. EAJA fees also granted at the statutory rate in the Third Circuit in Johnson v. Gonzales, No. 03-1931 (3d Cir. July 25, 2005) (82 hours of work plus $550 in costs yields around a $10,800 award).