(a) No company shall act as a fiduciary in this state except:

(1) A state trust company;

(2) A state bank authorized to act as a fiduciary;

(3) A savings association or savings bank organized under the laws of this state and authorized to act as a fiduciary;

(4) A national bank having its principal office in this state and authorized by the comptroller of the currency to act as a fiduciary pursuant to 12 U.S.C. § 92a;

(5) A federally chartered savings association or savings bank having its principal office in this state and authorized by its federal chartering authority to act as a fiduciary;

(6) An out-of-state bank with a branch in this state established or maintained pursuant to this chapter, or a trust office authorized by the commissioner pursuant to this chapter;

(7) An out-of-state trust company with a trust office authorized by the commissioner pursuant to this chapter;

(8) A foreign bank with a trust office authorized by the commissioner pursuant to this chapter; or

(9) A private trust company to the extent authorized by the commissioner pursuant to this chapter.

(b) No company shall engage in an unauthorized trust activity. No company shall be deemed to be subject to this chapter and chapter 1 of this title, regulating fiduciary activities to the extent that the company's activities are permitted by existing statutory authority or are customarily performed as a traditional incident to the company's regular business activities.

(c)

(1) A bank authorized to act as a fiduciary, which includes a trust company for the purposes of this section and §§ 45-2-1002 — 45-2-1006, having and maintaining paid-in capital and surplus of five hundred thousand dollars ($500,000), may be appointed a fiduciary or cofiduciary by any person or any court having jurisdiction and authority to appoint fiduciaries.

(2) When appointed as a fiduciary for a minor or other incompetent person, a bank shall have only the custody, control, management and administration of the property or estate of the person.

(3) The personal care and custody of any minor or other incompetent person shall be committed and confided to those individuals who would otherwise be entitled by law to the guardianship or care and custody of the person of the minor or incompetent person.