Yehudayona…
” I wonder what would happen with the grandchildren of those who were last domiciled in New York if the parents are U.S. citizens who never lived in the U.S.”
The grandchildren would NOT be US citizens!
If you look at the US Citizens and Immigration Services website section on ‘Citizenship through Parents’ you will find the law requires that the parent have had lived in the USA or its territories:
Both parents are U.S. citizens at the time of birth,
At least one parent lived in the U.S. or its territories prior to the birth.
One parent is a U.S. citizen at the time of birth and the birthdate is on or after November 14, 1986
The U.S. citizen parent had been physically present in the U.S. or its territories for a period of at least five years at some time in his or her life prior to the birth, of which at least two years were after his or her 14th birthday.
If the U.S. citizen parent spent time abroad in any of the following three capacities, this can also be counted towards the physical presence requirement:
Serving honorably in the U.S. armed forces;
Employed with the U.S. government; or
Employed with certain international organizations.
Additionally, time spent abroad by the U.S. citizen parent while the U.S. citizen parent was the unmarried son or daughter and a member of the household of a person who meets any of the three conditions listed above can also be counted.
AND…
The genetic or non-genetic gestational legal mother is a U.S. citizen at the time of birth, and the birth date is after December 23, 1952 The mother had previously been physically present in the United States or one of its outlying possessions for a continuous period of at least one year.
The genetic father is a U.S. citizen at the time of birth, the mother is an alien, and the birthdate is on or after November 14, 1986
A blood relationship between the person and the father is established by clear and convincing evidence,
The father (unless deceased) has agreed in writing to provide financial support for the person until the person reaches the age of 18 years, and
While the person is under the age of 18 years one of the following occurs:
The father acknowledges paternity of the person in writing under oath, or
The paternity of the person is established by adjudication of a competent court, and
The U.S. citizen parent was physically present in the U.S. or its territories for a period of at least 5 years at some time in his or her life prior to the birth, at least 2 of which were after his or her 14th birthday.
If the U.S. citizen parent spent time abroad in any of the following three capacities, this can also be counted towards the physical presence requirement:
Serving honorably in the U.S. armed forces;
Employed with the U.S. government; or
Employed with certain international organizations.
Additionally, time spent abroad by the U.S. citizen parent while the U.S. citizen parent was the unmarried son or daughter and a member of the household of a person who meets any of the three conditions listed above can also be counted.