Adiyen has the below points to add on the origin of the Pallavas:
Firstly, there is no clear consensus among scholars on their origin. There are some who claim that Pallavas are related to the Persian Pahlavi dynasty who are called Pahlavas in Farsi. This is ahuge stretch of imagination to link these two dynasties based on linguistic similarty of name.
The Pallavas themselves referred to themselves as descendents of Brahma of the Bhradwaja gotra, dorectly descended from Aswattama, son of the Mahabharata character Drona (see Nellur inscription and Vellur Palaiyam inscription). This is interesting because all other dynaties of the time claimed lineage from the Solar or Chandra dynasty. Interestingly also, the only instance of Brahma worship (within context of Trimurti temples was found only during Pallava period - giving strength to the importance they placed on Brahma the creator God). Some have tried to use this to claim the Pallavas were Brahmin kings. This may be so. However, this fact is never mentioned either in inscriptions or any other source which is strange. So they were probably not brahmins.
Since their pattayams were exclusively in prakrit and sanskrit, it is said that they were northerners. This is possible but the evidence is not overwhelming.
On the other hand, there is a claim by Rajanayakam that pallavars were from mani pallavam and descended from Ilanthiraiyan Thondaiman. This is exciting but has no real evidence to support it.
Some say that Pallavas were not Tamils because they were not mentioned with Chera Chola Pandiyar in Sangam literature but this is quite specious. Not mentioned does not mean that they were not Tamils or people of the South. Maybe a stronger thing to say is that none of the Pallavas had Tamil names as for Sangam kings. This is a good point.
I think the best hypothesis is by Krishnasamy Iyengar, Sathyanadayyar and Ragavayangar who say that they were probably minor Telugu chieftains under the Sadavhanas who after the decline of the Sadavahana dynasty took over. This theory is supported by the fact that there was no major invasion recorded in Thondai mandalam lending credence to the fact that the Pallavas were indigenous even if not entirely 'local'.
In fine, the Pallavas were very possibly a Telugu branch of Sadavahanas or local Tamil chiefs who took over. Either way they were Southerners.
Perhaps it is useful to note that at the time in question, there was no clear idea of Tamizhar, people tended to identify themselves as Pandiyas. Chozhas, Pallavas and so on. Most importantly, by the time of Nandivarman III, the Pallavas saw themselves and were seen to Tamil kings - see Nandi kalambakam.