So, I did a little digging for ya.
I think this answers your questions-
R12-4-304D. An individual may take predatory and furbearing animals
by using the following methods, subject to the restrictions
in R12-4-318:
1. Firearms not prohibited in R12-4-303;
2. Bow and arrow;
3. Crossbow;
4. Traps not prohibited by R12-4-307; and
5. Artificial light while taking raccoon, if the light is
not attached to or operated from a motor vehicle,
motorized watercraft, watercraft under sail, or floating
object towed by a motorized watercraft or a
watercraft under sail.
R12-4-303
Unlawful Devices, Methods, and Ammunition
A. In addition to the prohibitions prescribed in A.R.S. §§
17-301 and 17-309, the following devices, methods, and
ammunition are unlawful for taking any wildlife in this
state. An individual shall not use or possess any of the
following while taking wildlife:
1. Fully automatic firearms, including firearms capable
of selective automatic fire;
2. Tracer, armor-piercing, or full-jacketed ammunition
designed for military use;
3. Shotguns larger than 10 gauge or shotguns capable
of holding more than five shells in the magazine,
unless plugged with a one-piece filler that cannot
be removed without disassembling the gun, and that
limits the magazine capacity to five shells;
4. Semiautomatic centerfire rifles with a magazine
capacity of more than five cartridges, unless the
magazine is modified with a filler or stop that cannot
be removed without disassembling the magazine;
5. Contrivances designed to silence, muffle, or minimize
the report of a firearm; (deleted irrelevant content)
It looks like there IS a magazine capacity for shotgun when hunting predators in AZ, and that limit is 5 rounds in the magazine...I'm glad I looked. Sorry if I mislead you.