Specifically addressing the question about what to answer for this question on the ESTA application:
H) Have you ever stayed in the United States longer than the admission
period granted to you by the U.S. government?
At the bottom of the page it is stated:
I, the applicant, hereby certify that I have read, or have had read to
me, all the questions and statements on this application and
understand all the questions and statements on this application. The
answers and information furnished in this application are true and
correct to the best of my knowledge and belief.
Given the applicant has overstayed as a minor, the expected truthful answer to this question would be yes. Answering no to this question would seem to require the applicant to have an implied admission period grant up until the age of majority.
According to INA: ACT 212 - GENERAL CLASSES OF ALIENS INELIGIBLE TO RECEIVE VISAS AND INELIGIBLE FOR ADMISSION as provied by @HermitCrab in comments:
(B) ALIENS UNLAWFULLY PRESENT.-
(i) In general.-Any alien (other than an alien lawfully admitted for
permanent residence) who-
(I) was unlawfully present in the United States for a period of more
than 180 days but less than 1 year, voluntarily departed the United
States (whether or not pursuant to section 244(e)) prior to the
commencement of proceedings under section 235(b)(1) or section
240, and again seeks admission within 3 years of the date of such
alien's departure or removal, or
(II) has been unlawfully present in the United States for one year or
more, and who again seeks admission within 10 years of the date of
such alien's departure or removal from the United States is
(ii) Construction of unlawful presence.-For purposes of this
paragraph, an alien is deemed to be unlawfully present in the United
States if the alien is present in the United States after the
expiration of the period of stay authorized by the Attorney General
or is present in the United States without being admitted or
(I) Minors.-No period of time in which an alien is under 18 years of
age shall be taken into account in determining the period of
unlawful presence in the United States under clause (i).
So (to my non-legal eyes), for the purposes of visa application, the minor has been not unlawfully present. Not having been unlawfully present and not having ever overstayed, are not the same thing however. It would seem to me, again as a non-lawyer, that if the applicant was not unlawfully present, they could not be deported, for example, but that is evidently not the case:
over 10 years ago i was deported from the USA for being an illegal
overstay BUT i was only 14-15 at the time
However, at least one lawyer claims this is not an overstay:
Generally, an overstay as a minor (with the deportation or exit
occurring before 18) would not be an "overstay" from an immigration
perspective. You should not encounter problems visiting the US. With
cases like these, I usually recommend that my clients carry with them
a legal opinion letter setting out the background information, the
above opinion, with regulations and precedent if needed, to back it
up. That way it almost indefinitely ensure passage into the US despite
Evidently there seems to be a conflict of opinion in researching this.
If this happened to me personally, I would answer yes to this question. If you intend on answering no, I think you would be advised to seek a legal opinion to back up your assertion in order to present it to the CBP officer at the port of entry.