This multi-layered saga seems to have been an epic tussle between Vishnu and Siva partisan story tellers.
This question is not a duplicate of the question
in answers to which questionable sources have been cited by posters.
This question asks for verifiable answers drawn only from canonical scriptures like major Puranas and seeks to leave an unbiased record of the sectarian escalation ladder on this topic.
hantum abyaagatam roudram sarabham narakEsaree /Nakhair vidaarayaamaasa hiraNyakasipum yathaa // (~varAha purAna)
Meaning: The half-man, half-lion (Narasimha) killed the violent Sharabha who had approached him (for battle) by lacerating Sharabha with his nails in a similar manner as in the case of Hiranyakasipu
(the Sanskrit is really mediocre in this citation - I don't see Vyasa writing such verse).
Vishnu purana doesn't being Siva into this at all - although it has Vishnu killing a Hiranyakashipu who had repented:
And the great Asura repented of his former cruelty, and treated him with kindness; and Prahlada, fulfilling his duties like any other youth, continued diligent in the service of his preceptor and his father. After his father had been put to death by Visnu in the form of the man-lion. Prahlada became the sovereign of the Daityas
Once Siva gets into the picture all kinds of outcomes arise:
(1) Sharabha kills/defeats Narasimha and the latter recovers his Satvika self and returns to the heavens. this is well documented in Puranas and in sculpture (like the UN World Heritage site Airavateswara temple )
(2) Either Narasimha or a fiercer form (Ganda Bherunda) kills Sharabha - this doesn't seem to be documented in canonical Puranas, although there are blogs that claim this version of events is in Vaishnavite Puranas.
(3) they are both pacified by Pratyangira Devi
(4) Other outcomes I am not aware of
Can someone post (only) what is in canonical Sanskrit scriptures about this matter (I am not interested in regional follow-up legends)?