Source : www kamakoti org/kamakoti/varaha/bookview.php?chapnum=5&PHPSESSID=fd2628395e9242651c5007180a137b0f
Pitaram-Haradasa Gothram-Narayana Murti Sharmanaam-Swadhaanamah Tarpayami (The last word to be uttered thrice and simultaneously tarpanam be left thrice as well)
Note: Tila or Sesame / Ginjelley seeds must be mixed with the water to be utilised for Tarpanam)
Pitaram-Father, Pitamaham- Grand Father, Prapitamaham-Great Grand Father, Mataram-Mother, Pitamahim- Father’s mother, Prapitamahim- Father’s Grand Mother, Sapnatimataram- Father’s another wife if applicable; if Karta (Performer) was adopted to another family then to his adopted parents viz. Janaka Pitaram and Janaka Mataram; Matamaham- Mother’s Father, Mathuh Pitamaham- Maternal Grand Father, Mathu Prapithamaham-Mother’s Great Grand Father, Matamahim- Mother’s Mother, Mathuh Pitamahim-Mother’s Grand Mother, Mathuh prapitamahim- Mother’s Great Grand Mother, Atma Patnim-Wife, Sutham- Sons, Bhrataram- Brothers, Pitravyam-Father’s Brothers, Mathulam- Maternal Uncles and their Wives, Duhitaram-Daughters, Bhagineem-Sisters, Dauhitram-Grand Sons, Bhagineyam- Nephews, Pitru Bhagineem- Father’s Sisters, Matru Bhagineem- Mother’s elder/younger Sisters, Jamatharam-Son in laws, Bhavukam- Brothers in laws and their wives, Snushaam-Daughter in law, Swasuram / Swasrum- Wife’s father/ mother, Syalakam-Wife’s brothers and their wives, Guru and Rikthinam- the Main Shop Keeper ( in fact ,wherever not mentioned tarpanam may be done as Sapatneekam or Sabhartreekam as the case may be, if the departed Souls are devoid of wives/husbands. As a round up-Evam Tarpanam kuryat: Echasrutkuley Jaata Aputhro gotrinomrutah, they gruhnanthu maya dattam sutra nishpeedanodakam
(May my Tarpanas be please accepted on behalf of those in our Vamsam, the Sagotras or those who died without sons by way of sqeezing water from my Yajnopaveeth; this Mantra be recited by wearing the Holy Thread as a mala or long necklace and be left in the Tarpana Plate)]
Instead of giving long list of names, we do it with the Gnyadagyaada vargadvaya pitrun. Your father or great-grand-father can offer tarpanam to your mother i.e. their wife or daughter-in-law respectively. As long as the father or grand-father and great-grand-father does tarpanam, the entire family tree is taken care of, thus no need for each member to do tarpanam.