Punabbhava: lit.: re-becoming; 'renewed existence', is a sutta term for 'rebirth', which, in later literature mostly is called patisandhi The attainment of Sainthood arahatta implying the end of future rebirths, is often expressed in the words:;This is the last birth. Now there is no more a renewed existence!; natthi dāni punabbhavo M. 26; D. 15; Therag. 87, 339; Sn. 502. - The term is often linked with abhinibbatti 'arising'.
But how, o brother, does it come to renewed existence and arising in the future āyatim punabbhavābhinibbatti? Because beings, obstructed by ignorance and fettered by craving, find ever fresh delight now here, now there, for this reason there is renewed existence and arising in the future; M. 43. See also S.XII. 38. abhinibbatti also stands sometimes alone in signifying 'rebirth', e.g. in A. VI, 61; X, 65.
Maha Thera Nyanatiloka. Manual of Buddhist Terms and Doctrines, Buddhist Publication Society, first edition 1952.