How many cc's of fat can legally be removed in Alabama?

For most places, it is probably best to limit the removal of fat to under 5000 cc's.  You did not include a picture, but it is rare to get that much out of the abdomen and back areas, at least, in my practice.

I am not sure if Alabama has specific limits on the amount of liposuction that can be removed or not. Some states have set limits for in office and outpatient surgery centers. I would check with the Alabama Board of Medicine if no surgeon from Alabama responds to this question.

From ASPS:"There is no scientific data available that supports a specific volume maximum at which point liposuction is no longer safe, although the risk of complications is unavoidably higher as the volume of aspirate and the number of anatomic sites treated increases." In general... if you liposuction more than 5000cc of aspirate....you should stay in the hospital overnight for monitoring. If your having liposuction to your back ...I do not forsee that coming close to 5000cc.Good luck.

Instead of considering the laval limits, please find a plastic surgeon who will do what is best for you. 

Florida is the only state that has specific limitations on fat removal if not done in an accredited surgery center.  There are however safe limits that should be discussed with you prior to surgery.  

Legally in a particular state is not the issue, the safety of the procedure is compromised above 5000cc removed. But if you have that much fat in your back (extremely unlikely) you would need a lot more done than simple liposuction.