20% has been accomplished according to their official website:
http://www.alkafeel.net/alkafeelnews/view.php?id=428

It is financed and belongs to al-Abbas Holy Shrine. They didnt mention a specific name for the hospital yet.

3 story building
135 beds
10 operation rooms


http://www.alkafeel.net/alkafeelnews/up2/428.jpg

http://www.alkafeel.net/alkafeelnews/up3/428-1.jpg

http://www.alkafeel.net/alkafeelnews/up3/428-2.jpg

http://www.alkafeel.net/alkafeelnews/up3/428-3.jpg

http://www.alkafeel.net/alkafeelnews/up3/428-5.jpg

from October 2012. I have bad feelings about the finishing.

http://www.imamhussain.org/report/big/34-1-778.jpg

http://www.imamhussain.org/report/big/34-4-778-3.jpg

http://www.imamhussain.org/report/big/34-6-778-5.jpg

http://www.imamhussain.org/report/big/34-8-778-7.jpg

http://www.imamhussain.org/report/big/34-10-778-9.jpg

http://www.imamhussain.org/report/big/34-12-778-12.jpg

http://www.imamhussain.org/report/big/34-17-778-15.jpg