They exist, but of course require a federal tax stamp, under the (blatantly unconstitutional) National Firearms Act. Unfortunately any made since 1986 can not have a stamp issued for their transfer to a civilian, under the (even more blatantly unconstitutional ban provision of the Firearms Owners Protection Act) Here's a video of one being fired. The AA12 Shotgun is currently being manufactured and marketed by Baber's company, Military Police Systems, Inc., a.k.a. MPS, Inc. (Phone: 423-534-2480), which is located in Piney Flats, Tennessee.
Here's a photo of it.
