Visiting the US after overstaying as a minor 13 years ago?

First and foremost I would suggest contacting am immigration attorney to get a more exact view of the situation.

Having said that the best information available is that you likely have not received the ban (All LAW) but your visa was canceled due to your overstay. So to the question of overstay you should answer YES.

It is also highly likely that you may not be eligible to use ESTA and a Visa Waiver program to enter the US and will need an actual visa, so instead of trying your luck at ESTA apply for a B2 visa.

P.S. I would again very strongly suggest contacting an immigration attorney since it may be possible that the laws in effect today may not be the same as they were in 2002.

Based on my experience, you don't need to get a Visa. I moved to the US in 2003 with a O-1 visa with my wife and my daughter. In 2006 my immigration lawyer forgot to add my wife and daughter on my visa renewal application. We voluntarily left in 2011 when my daughter was 11, so she overstayed almost 4 years. My daughter went to the US three times on vacation just with the ESTA. No problem at all. On the other hand, my wife who has a 10 year bar was denied her B2 visas twice. The US immigration law clearly says that overstaying as a minor doesn't count.

Edited in from comment:

212(a)(9)(B) ALIENS UNLAWFULLY PRESENT (iii) Exceptions (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.

Source

I have two more pieces of info to add to what has already been said:

• I applied for ESTA back in 2013 and for curiosity looked back on my form from back then. There was no question about previous overstays in 2013. So likely the poster of this answer never came across this question for his daughter.

• I emailed CBP about your question whether to tick yes even though overstays as minors don't accrue unlawful presence. The answer was quite clear:

Good Day,
You would answer the question as it appears, even if you were a minor. Each situation is considered on it's own merit but you must provide accurate information.
Thank you,

So clearly, you should answer yes about previous overstays, even those as a minor.

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 inadmissible.

(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 paroled.

(iii) Exceptions.-

(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 this issue.

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.

In your shoes, I would admit to the facts, and "argue" the legal implications.

That is to say that you should tick yes on the ESTA form and admit that you "stayed in the United States longer than the admission period granted to you by the U.S. government," give the relevant dates, and relate them to your ages at the time.

You can then deny an "illegal" presence by quoting the law about "Aliens Unlawfully Present," that says,

"iii) Exceptions.-

(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)."

That is, you claim that your "overstay," while factual, was not illegal because of your age, and the fact that you were in the company of your parents.

Someone who understood all the implications would "wave you through." If you feel more comfortable, hire an immigration lawyer and have him/her advise you on the application and represent you to the immigration authorities.

It was not an "immigration" matter, but I once "got off" after self-reporting a "technical" violation of rules that was due to circumstances beyond my control. (The matter was shortly thereafter resolved in my favor.) I felt that this was far better than having the authorities find out afterwards on their own, because then I wouldn't be able to plead "extenuating circumstances."