Paraśurāma Kalpasūtra, in Gaṇanāyaka paddhati, states:
सर्वत्र देवतानामसु श्रीपूर्वं पादुकामुच्चार्य पूजयामीत्यष्टाक्षरं योजयेत् |
This means that the mantra to be employed during worship is: (dēvatānāma)+śrīpādukāṁ pūjayāmi.
Some here think this is indicative of pūjana alone (i.e. puṣpākśatā prakṣēpa) and not of tarpaṇa (or more specifically bindu-prakṣēpa). However, one should observe the next sūtra:
एवं पञ्चावरणीमीष्ट्वा पुनर्देवं गणनाथं दशधोपतर्प्य |
‘punaḥ’ upatarpya – clearly indicates that tarpaṇa is intended even in the former sūtra.
In śrīkrama, the sūtra states:
मूलेन त्रिधा सन्तर्प्य |
Here, Rāmēśvara states that, unlike other places where there is bindupuṣpākṣatōbhaya-prakṣēpa, here the prescription is for bindumātra-prakṣēpa. Hence, even if pūjayāmi is the general sanction based upon the sūtra quoted before, here tarpayāmi should be used based on the pramāṇa from Dakṣiṇāmūrti Samhitā:
स्वाहा होमे तर्पणे च तर्पयामीति चोच्चरेत् |
Umānandanātha accepts the pramāṇa of tantrāntara and uses the format:
पूजयामि तर्पयामि नमः |
This, according to some authorities, violates the intention of the sūtrakāra as pointed out by Rāmēśvara. He points out that when the prescription is to exclusively offer viśēṣārghya-bindu, it constitutes tarpaṇa. In such select few places, for e.g. Mūladēvatā tarpaṇa in the Bindu, etc., the format of the mantra used would be:
श्रीपादुकां तर्पयामि |
When the instruction is for pūjā, it means offering viśēṣārghya-bindu along with puṣpākṣata. Technically, this does not constitute tarpaṇa. The intention of offering arghyabindu along with puṣpākṣata is of pūjana and hence the format, according to him, would be:
श्रीपादुकां पूजयामि |
Tantrarāja also prescribes the use of saptākśarī everywhere (pādukāṁ pūjayāmi).
Some follow the format tarpayāmi namaḥ with the assumption that ‘namaḥ’ is indicative of pūjana, but there seems to be no śāstra pramāṇa for such an assumption.
If one observes popular practice today, the usage is: śrīpādukāṁ pūjayāmi tarpayāmi namaḥ, which is based on the Dakṣiṇāmūrti Samhitā. That this is sāmpradāyika is affirmed by the following:
पूजयामि तर्पयामि नमोऽन्तं केरळे मतम् |
तर्पयामि पूजयामि नमः काश्मीरगोचरः ||
Kēralācāra is Dakṣiṇācāra and the format here, based on sampradāya is: pūjayāmi tarpayāmi namaḥ. Though not specified here, in Gauḍa sampradāya, the format is pūjayāmi namaḥ tarpayāmi namaḥ. In Kāśmīrācāra, the usage is: tarpayāmi pūjayāmi namaḥ.