Gonna be long one
The ATF FAQ used to include all of this before it was redesigned:
Q: May I transfer the receiver of a short-barrel rifle or shotgun to an FFL or to an individual as I would any GCA firearm?
A: Yes. A weapon that does not meet the definition of a NFA firearm is not subject to the NFA and a possessor or transferor needn't comply with NFA requirements. The firearm is considered a GCA firearm and may be transferred under the provisions of that law.
Q: Who is responsible for notifying the NFA Branch when I transfer the GCA firearm to a FFL or another individual?
A: There is no requirement that the transferor or transferee of a GCA firearm notify the NFA branch of a transfer or that either party determine whether the firearm was previously registered under the NFA. There is no also no requirement for the registrant or possessor of a NFA firearm to notify ATF of the removal of features that caused the firearm to be subject to the NFA; however, ATF recommends the owner notify the NFA Branch in writing if a firearm is permanently removed from the NFA.
Q: What is the registered part of a Short Barreled Rifle (SBR) or Short Barreled Shotgun (SBS)?
A: While a receiver alone may be classified as a firearm under the Gun Control Act (GCA), SBRs and SBSs are classified in totality under the National Firearms Act (NFA). A firearm that meets the definition of a SBR consists of a rifle that has a barrel less than 16 inches in length. A SBS consists of a shotgun that has a barrel less than 18 inches in length. The serialized receiver is recorded for registration in the National Firearms Registration and Transfer Record (NFRTR).
Q: I possess a properly registered SBR or SBS. I intend to strip the receiver and remove the barrel prior to selling the receiver. Is the bare receiver still subject to regulation under the NFA as a SBR or SBS?
A: A stripped receiver without a barrel does not meet the definition of a SBR or SBS under the NFA. Although the previously registered firearm would remain registered unless the possessor notified the NFA Branch of the change, there is no provision in statute or regulation requiring registration of a firearm without a barrel because its physical characteristics would make it only a GCA firearm pursuant to 18 U.S.C. § 921(a)(3)(B). If the subsequent owner buys the receiver as a GCA firearm and installs a barrel less than 16 inches in length (SBR) or 18 inches in length (SBS), the firearm would be subject to a $200 making tax and registration under the NFA by the manufacturer or maker of the SBR or SBS. Because registration depends upon the stated intent of the applicant, there is no provision to allow registration of a NFA firearm by anyone other than the maker or manufacturer.
Q: If I remove the short barrel from the registered SBR or SBS, is the receiver still subject to NFA transfer and possession regulations?
A: If the possessor retains control over the barrel or other parts required to assemble the SBR or SBS, the firearm would still be subject to NFA transfer and possession regulations. ATF recommends contacting State law enforcement officials to ensure compliance with state and local law.
Q: Does the installation of a barrel over 16 inches in length (SBR) or 18 inches in length (SBS) remove the firearm from the purview of the NFA? If so, is this considered a permanent change?
A: Installation of a barrel greater than 16 inches in length (SBR) or 18 inches in length (SBS) will remove the firearm from the purview of the NFA provided the registrant does not maintain control over the parts necessary to reconfigure the firearm as a SBR or SBS.
