(adjective) / not disqualified on any of the grounds described in SCPA § 707 (SCPA § 103 [18])
Plain English translation: Anyone who is not disqualified by statute, is considered eligible to serve as a fiduciary (e.g. administrator, executor, guardian, trustee). The statute that tells us who is disqualified is SCPA § 707.
SCPA § 707
(1) Persons ineligible:
(a) Infant
(b) An incompetent
(c) A non-domiciliary alien except one who is a foreign guardian as provided in subdivision four of section one thousand seven hundred sixteen of this chapter, or one who shall serve with one or more co-fiduciaries, at least one of whom is a resident in this state. Any appointment of a non-domiciliary alien fiduciary or a New York resident fiduciary hereunder shall be made by the court in its discretion.
(d) A felon
(e) One who does not possess the qualifications required of a fiduciary by reason of substance abuse, dishonesty, improvidence, want of understanding, or who is otherwise unfit for the execution of the office
(2) Persons ineligible in court’s discretion: the court may declare ineligible to act as a fiduciary a person unable to read and write the English language. 
Example: Laura is Rob’s widow. Laura’s criminal record contains a felony. Therefore, Laura is ineligible to serve as executor of Rob’s estate.

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Samantha M. Sbrocchi
Helping clients in New York and New Jersey with various probate, administration and estate litigation matters.