Amavasya Shraddha could be performed for those souls who have departed on Amavasya Tithi or Krishna Paksha (Dark Fortnight).
If someone has not been able to perform last rituals on all these days then, Amavasya Shraddha is the last resort for performing such rites.
Amavasya Shraddha is performed for all those who died on any unknown day or date. On this day people perform Shraddha for all their ancestors.
So, Amavasya Shraddha is also known asSarvapitra Moksha Amavasya.
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Mahalaya Shraddha for those who died on Purnima Tithi is also done on Amavasya Shraddha Tithi and not on Bhadrapada Purnima. Although Bhadrapada Purnima Shraddha falls one day before Pitri Paksha but it is not part of Pitri Paksha. Usually Pitri Paksha starts on the next day of Bhadrapada Purnima Shraddha.
In West Bengal, Mahalaya Amavasya Shraddha is considered to be the beginning of Navaratri Festival. It is believed that Goddess Durga was descended on the Earth on this day.
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Pitri Paksha or Mahalaya Shraddhas are Parvan Shraddhas(पार्वणश्राद्ध) and auspicious time to perform them is Kutup Muhurt and Rohina Muhurt.
It could be performed till Aparahna Kala (Post Meridian) gets over.
Tarpan (तर्पण) could be performed at the end of the Shraddha.
Tarpana is performed with Til, water and other materials by offering to ancestors. Tarpana could be performed on any day but on Shraddha these are usually performed at the end.