Branches of Rigveda are explained in Vishnu Purana. Vishnu Purana’s fourth chapter in Part three mentioned about the branches of Rigveda.
At the beginning of creation, Rigveda contained all the four Vedas with hundred thousand mantras. That Rigveda helped a lot in the propagation of ten kinds of Yagyas.
Then during the twenty-eighth Dwapar, my son, Krishnadwaipayan effected the division of Rigveda in four Vedas. At the same time, he also trained four of his distinguished disciples in the study of Vedas. Each one of them was interested with the study of one particular Veda for infinite period of time.
Accordingly, sage Pail mastered in Rigveda, Vaishampayan in Yajurveda, Jaimini in Samaveda and Sumantu in Atharvaveda. With the four Vedas, practice of Chaturhotra also came into being. Chaturhotra is now the main guiding feature of all kinds of Yagyas. Vyasa also established the Karmas of Adhvarayu by Yajurveda, of Hota by Rigveda, of Udgata by Samaveda and of Brahma by Atharvaveda.
Sage Pail divided Rigveda into two divisions and taught them to two of his disciples- Indrapramiti and Vashkal. In his term, Vashkal divided his branch into four sub-branches and taught them to his disciples. Indrapramiti taught his branch of Rigveda to his talented son, sage Mandukeya. Thus branches and sub-branches of Rigveda grew substantially. In this tradition, Shakalyavedamitra learnt a Samhita and divided it into five sub-branches. One of his disciples named Shakpurn created three Samhitas whereas his another disciple created Nirukta Grantha. Vashkal created three Samhitas and taught them to Kalayani, Gargya and Tathaja.