Wikipedia:

Model A

The Auto & Burglar Gun was manufactured in two variations. Approximately 2,500 of the original variation were manufactured from 1921 to 1925 using Ithaca’s standard 20 gauge Flues model shotgun, and designed to fire 2½” shells. Sometimes referred to as “Model A”, its barrels were about 10″ in length. These guns should only be fired with 2½” shells; firing longer shells will “bulge” the barrels.

Flues model

The Flues model was designed with a “saw handle” style grip featuring a large spur at the top to absorb recoil.
New Improved Double model

Ithaca redesigned the gun in 1925 using its New Improved Double (NID) model shotgun, which fires 2¾” shells; the barrels were lengthened to about 12.2″; and the grip was redesigned without the spur. Sometimes referred to as “Model B,” about 1,500 were manufactured. Model A and Model B are not formal factory designations.

Demise

Ithaca stopped manufacturing the Auto & Burglar Gun when it became subject to registration and a $200 transfer tax under the National Firearms Act (NFA) of 1934 (the transfer tax was reduced to $5 in 1960). Relatively few Auto & Burglar Guns were manufactured, and they are today highly prized as collector’s items. Approximately 20 Auto & Burglar Guns were specially manufactured, representing .410 bore, 28 gauge, and 16 gauge, only 11 of which have been reliably documented, and all these guns are extremely rare. The earliest known Ithaca Auto & Burglar Gun was manufactured about 1921, possibly as a prototype; it bears serial number 354442; is in 28 gauge with 12″ barrels; “Auto & Burglar Gun” is hand-engraved on each side; and the gun is listed separately in the Firearms Curios or Relics List published by the Bureau of Alcohol, Tobacco, Firearms and Explosives.

While it is sometimes incorrectly identified as a “sawed-off shotgun,” the Ithaca Auto & Burglar Gun is a smooth bore pistol which since 1934 has been classified as an “Any Other Weapon” (AOW) under the NFA, and it must be registered with the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF). Auto & Burglar Guns that are not currently registered are contraband, and cannot be legally possessed or registered. The penalties for illegal possession include up to a $250,000 fine and 10 years in prison.

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Auction sales estimates range from $2500 to $8000. Expect to pay nearer the latter.