Perfromance of rites to departed kin

Who Should Perform Cremation and death rites for a deceased person  according to Dharmasastras, as quoted in the Smriti Mukthaphalam   Sraddhakaandam   authored by Vaidyanatha Deekshita.

क्रमेण प्रेतकार्यकर्तॄनाह मरीचिः

पुत्रः पौत्रश्च तज्जश्च पुत्रिकापुत्र एव च पत्नी भ्राता च तज्जश्च पिता माता स्नुषा तथा॥भगिनी भागिनेयश्च सपिण्डो धनहार्यपि। पूर्वपूर्वविनाशे स्युरुत्तरोत्तरपिण्डदाः।  ईति

पराशरोऽपि –

पुत्रः पौत्रः प्रपौत्रो वा तद्वद्वा भ्रातृसन्ततिः इति।

कालदर्शोऽपि –

दाहादिमंत्रवत् पित्रोर्विदध्यादौरसः सुतः। तदभावे तु पौत्रश्च प्रपौत्रः पुत्रिकासुतः॥ इति।

क्षेत्रजो दत्तकः क्रीतः कृत्रिमो दत्त एव वा। अपविद्धश्च पत्नी  च गूढजः कन्यकासुतः।

पौनर्भवः सहोढोन्यो नंदनश्च सुतीकृतः। दौहित्रो धनहारी च भ्राता तत्पुत्र एव वा।

 पिता माता स्नुषा चैव स्वसा तत्पुत्र एव च। सपिण्डः सोदको मातुः सपिण्डश्च सहोदरः।

स्त्री च शिष्यः ऋत्त्विगाचार्या जामाता च सखापि वा उत्सन्नबन्धो रिक्थेन कारयेदवनीपतिः।

krameṇa pretakāryakartṝnāha marīciḥ

putraḥ pautraśca tajjaśca putrikāputra eva ca patnī bhrātā ca tajjaśca pitā mātā snuṣā tathā||bhaginī bhāgineyaśca sapiṇḍo dhanahāryapi| pūrvapūrvavināśe syuruttarottarapiṇḍadāḥ|  īti

parāśaro'pi --putraḥ pautraḥ prapautro vā tadvadvā bhrātṛsantatiḥ iti|

kāladarśo'pi --dāhādimaṁtravat pitrorvidadhyādaurasaḥ sutaḥ| tadabhāve tu pautraśca prapautraḥ putrikāsutaḥ|| iti|

kṣetrajo dattakaḥ krītaḥ kṛtrimo datta eva vā| apaviddhaśca patnī  ca gūḍhajaḥ kanyakāsutaḥ|

paunarbhavaḥ sahoḍhonyo naṁdanaśca sutīkṛtaḥ| dauhitro dhanahārī ca bhrātā tatputra eva vā|

 pitā mātā snuṣā caiva svasā tatputra eva ca| sapiṇḍaḥ sodako mātuḥ sapiṇḍśc sahodaraḥ|

strī ca śiṣyaḥ ṛttvigācāryā jāmātā ca sakhāpi vā utsannbandho rikthena kārayedavanīpatiḥ|

Mareechi has mentioned the order of duty of performing the death rites.

1.Son.  2.Son’s Son  3. Son’s Son’s Son.  4..The Son of a daughter who by an earlier verbal contract and provision of funds has been assigned this duty. 4. Wife 5. Brother. 6.Brother’s Son(s)  (7) Father  (8) Mother (9) Daughter in law. (10) Sister (11) Sister’s Son (12) Sapinda  (paternal relatives of three generation) (13) One who is inheriting the wealth of the deceased by testament or otherwise.   Among the foregoing categories, the persons mentioned ealier in the list  have the duty and on their absence/death alone the next persons take over.

Parasara has simply mentioned..

the duty is for the  Son, Son’s Son, Son’s Son’s Son or of equal status like the brother’s son etc.

The Lawgiver Kaaladharsa has  given very detailed hierarchy.

(1) the uterine Son   ( 2) Son’s Son  (3) Son’s Son’s Son  (4) Putrika the daughters son who is contracted for this purpose. (5) Son born in the womb of the deceased’s wife as Kshetraja (6) Adopted son  (7) a child who is purchased for a price. (8) Who has come as a dependent orphan and has been treated as a son (9) own son who has been given in adoption  (10) recognized as son though illegitimate  (11) Wife  (12) Son Who is born secretly (13) Son who was born when the wife was a virgin (14) Son born on a widow on remarriage (15) A boy living with him  (16) a boy who has been treated as son out of affection (17) Daughters son (18) The person who inherits the wealth. (19) Brother (20) Brothers Son (21) Father 

(22) Mother (23) Daughter in law (24) Sister (25) Sisters Son (26) Sapinda (three generation patrilinear male relative) (27) Sodaka ( seven generation patrilinear relative) (28) Sapinda on mother’s side (29) Mother’s Brother  (30) Maid servant (31) Disciple (32) The deceased preceptor the ritwig (33)  The deceased preceptor  aacharya (34)  Sisters husband (35) Friend  and  (36) for whom there are no relatives or the persons mentioned in the above categories, the ruler of the country has to arrange for creamation and aparakriya.