Form 4473
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Form 4473 is an ATF form that is required to be filled out by someone wishing to purchase a firearm from a federal firearm liscensed dealer (FFL).
It contains the customer's personal information as well as the make/model/serial number of the firearm. FFLs are required by the ATF to store these forms for as long as they remain in business. If the dealer goes out of business he is required to turn over these forms to the ATF. Many people consider the use of these forms to be an inefficient form of defacto gun registration.
However if you purchase a firearm from a private individual as opposed to a licensed dealer you are not required to fill this form. This however assumes you live in a state that allowes private individuals to sell firearms without having to go through a dealer. At present most states still allow private transfer of firearms.