AFAIK (I'm not to keen on NC laws)...
NC law prohibits the transfer of certain type of weapons to a minor (person under the age of 18), but rifles and shotguns are not prohibited. [NCGS 14-315]
NC "safe storage" law prohibits a minor (person under the age of 18) from having access to a firearm, unless the minor has (written) permission from their parent/legal guardian. [NCGS 14-315.1]
NC law prohibits a child (under the age of 12) from possessing a firearm. [NCGS 14-316 (a)]
Therefore...
It is legal for you give ownership of a shotgun to your child (needs to be older than 12).
It is legal to store a loaded shotgun in you home and allow your child (needs to be older than 12) to have access to that shotgun, as long as that child has written permission from you stating he is allowed to have access to it. The firearm will need to be stored in such a way that only the person who has permission to access it, can access it.
North Carolina General Statue 14-315
(a) Sale of Weapons Other Than Handguns. – If a person sells, offers for sale, gives, or in any way transfers to a minor any pistol cartridge, brass knucks, bowie knife, dirk, shurikin, leaded cane, or slungshot, the person is guilty of a Class 1 misdemeanor and, in addition, shall forfeit the proceeds of any sale made in violation of this section.
(a1) Sale of Handguns. – If a person sells, offers for sale, gives, or in any way transfers to a minor any handgun as defined in G.S. 14‑269.7, the person is guilty of a Class H felony and, in addition, shall forfeit the proceeds of any sale made in violation of this section. This section does not apply in any of the following circumstances:
(1) The handgun is lent to a minor for temporary use if the minor's possession of the handgun is lawful under G.S. 14‑269.7 and G.S. 14‑316 and is not otherwise unlawful.
(2) The handgun is transferred to an adult custodian pursuant to Chapter 33A of the General Statutes, and the minor does not take possession of the handgun except that the adult custodian may allow the minor temporary possession of the handgun in circumstances in which the minor's possession of the handgun is lawful under G.S. 14‑269.7 and G.S. 14‑316 and is not otherwise unlawful.
(3) The handgun is a devise and is distributed to a parent or guardian under G.S. 28A‑22‑7, and the minor does not take possession of the handgun except that the parent or guardian may allow the minor temporary possession of the handgun in circumstances in which the minor's possession of the handgun is lawful under G.S. 14‑269.7 and G.S. 14‑316 and is not otherwise unlawful.
(b1) Defense. – It shall be a defense to a violation of this section if all of the following conditions are met:
(1) The person shows that the minor produced an apparently valid permit to receive the weapon, if such a permit would be required under G.S. 14‑402 or G.S. 14‑409.1 for transfer of the weapon to an adult.
(2) The person reasonably believed that the minor was not a minor.
(3) The person either:
a. Shows that the minor produced a drivers license, a special identification card issued under G.S. 20‑37.7, a military identification card, or a passport, showing the minor's age to be at least the required age for purchase and bearing a physical description of the person named on the card reasonably describing the minor; or
b. Produces evidence of other facts that reasonably indicated at the time of sale that the minor was at least the required age.
North Carolina General Statue 14-315.1
(a) Any person who resides in the same premises as a minor, owns or possesses a firearm, and stores or leaves the firearm (i) in a condition that the firearm can be discharged and (ii) in a manner that the person knew or should have known that an unsupervised minor would be able to gain access to the firearm, is guilty of a Class 1 misdemeanor if a minor gains access to the firearm without the lawful permission of the minor's parents or a person having charge of the minor and the minor:
(1) Possesses it in violation of G.S. 14‑269.2(b);
(2) Exhibits it in a public place in a careless, angry, or threatening manner;
(3) Causes personal injury or death with it not in self defense; or
(4) Uses it in the commission of a crime.
(b) Nothing in this section shall prohibit a person from carrying a firearm on his or her body, or placed in such close proximity that it can be used as easily and quickly as if carried on the body.
(c) This section shall not apply if the minor obtained the firearm as a result of an unlawful entry by any person.
(d) "Minor" as used in this section means a person under 18 years of age who is not emancipated.
North Carolina General Statue 14-316
(a) It shall be unlawful for any parent, guardian, or person standing in loco parentis, to knowingly permit his child under the age of 12 years to have the possession, custody or use in any manner whatever, any gun, pistol or other dangerous firearm, whether such weapon be loaded or unloaded, except when such child is under the supervision of the parent, guardian or person standing in loco parentis. It shall be unlawful for any other person to knowingly furnish such child any weapon enumerated herein. Any person violating the provisions of this section shall be guilty of a Class 2 misdemeanor.