I'll just repost here the excellent explanation of Ven.Dhammanando at E-Sangha:
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Idappaccayatā = idaṃ + paccaya + tā.
‘Idaṃ’ means ‘this’, being the neuter nominative or accusative singular of the adjective/pronoun ‘ima’. However, when ‘idaṃ’ occurs in a compound word, with elision of the niggahīta, it may stand for any of the oblique cases of ‘ima’. Here it is understood by the commentators to stand for ‘imesaṃ’, the genitive plural — ‘of these’.
‘Paccaya’ = ‘paccayā’ (nominative plural) — conditions.
The suffix ‘-tā’ forms a noun of state, like the English ‘-ness’.
Literally: “conditions-of-these-ness”.
Intelligibly: “state [of being] the conditions of these”, where ‘these’ denotes old age, sickness, death and all the other items comprehended within the paṭiccasamuppāda formula.
So, that's one commentarial parsing of it. In another, less favoured by English translators, the suffix -tā is treated as redundant and so we get “idappaccayā eva” (“just the conditions of these”).
Maurice Walshe (Long Discourses): “the conditioned nature of things.”
Bodhi/Ñāṇamoli (Connected Discourses, Middle Length Discourses etc.): “specific conditionality.”
U Thittila (Book of Analysis): “specific causality.”
Pe Maung Tin (The Expositor): “specifically assignable causality.”
I think the last one is the best.
More from Pe Maung Tin, in his translation of the Dhammasaṅganī Atthakathā:
‘dvādasapadikaṃ paccayavaṭṭaṃ atthi nu kho natthī’ ti kaṅkhanto __idappaccayatāpaṭiccasamuppannesu dhammesu kaṅkhati_ nāma. tatrāyaṃ vacanattho — imesaṃ jarāmaraṇādīnaṃ paccayā ‘idappaccayā’. idappaccayānaṃ bhāvo ‘idappaccayatā’. idappaccayā eva vā ‘idappaccayatā’ ; jātiādīnametaṃ adhivacanaṃ. jātiādīsu taṃ taṃ paṭicca āgamma samuppannāti ‘paṭiccasamuppannā’. idaṃ vuttaṃ hoti — idappaccayatāya ca paṭiccasamuppannesu ca dhammesu kaṅkhatīti.
(DhsA. 355)
In doubting thus: ‘Is there, or is there not the round of the twelve causes?’ he is said to doubt these causally generated dhammas. Herein the word-definition is: ‘The causes of these dhammas, decay and death etc., are specifically assignable causes.’ ‘Specifically assignable causality’ is the state of such assignable causes. The two expressions are identical, and are synonyms here of birth etc. Birth and the rest of the series are said to be causally generated in the sense ‘come to pass because of, in consequence of.’ Or, he doubts the specifically assignable causation of dhammas which are causally generated.
(Expositor II. 458)
Best wishes,
Dhammanando Bhikkhu
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Metta, Dmytro