There is a Machloket between the Sephardim and the Ashkenazim as to exactly who lights the Menorah.
According to the Sephardim, the Ba’al Habayit (the head of the household) lights one Menorah. When he lights the Menorah he is representing all the inhabitants of the house, and he is fulfilling the Mitzvah for them. The rest of the family does not light once the head of the household lights. This is based on the opinion of how the Tosafot (various scholars of the 12th and 13th centuries) understood the Gemara.
Ashkenazim hold differently. Every member in an Ashkenaz family lights his own Menorah. This is based on the opinion of how HaRambam (Rav Moshe ben Maimon 1135-1204) understood the Gemara.
The Sha’arei Teshuva written by Rav Chaim Mordechai Margoliyot (in the 1800s) brings down from the Taz (Rabbeinu David HaLevi 1586-1667) that we have here a rare situation whereby Sephardim follow the Tosafot and the Ashkenazim follow HaRambam. We do not find this in any another place.
So there is an interesting question about a Sephardi who is away from home studying. For example, a young man who lives in New York may be in Israel studying for the year. Should this student light the Menorah on his own in the Yeshiva in Israel, or can he rely on the Menorah that is being lit by the head of his household back in New York?
Chacham Ovadia Yoseph addresses this question in Yichave Da’at, in Helek 6, siman 43. He comes out clearly that the Sephardic student who is away from home does in fact rely on the lighting made by the head of household even if he is 5000 miles away. This Sephardic young man does not light in the Yeshivah or in his dormitory. But if he wants to be Machmir, he may light without a Beracha, and that would be advisable. (See Torat HaMoadim, siman 2:7)
The Halacha is different for an Ashkenazic student. The Ashkenazim each light for themselves, and so the Ashkenazi student will light when away from home and with a Beracha.
This principal of relying on the head of household applies to Sephardim in all cases when they are away from home. The head of household or substitute, lights the Menorah, and that lighting would count for all the members of the house no matter where they are. (For additional details, see the Daily Halacha entitled "Chanukah- The Requirement of Lighting Falls Upon The House.")
