The Vatsīputrīya sect of Buddhism is an offshoot of the Vibhajyavāda that arose during the reign of Aśoka. It was later referred to as "Saṃmitīya." The followers of Vatsīputrīya took up a version of the position of the earlier Pudgalavādins, claiming that there was a real "person" underlying processes such as karma and rebirth.
The group consists of the Vatsiputriya, the original Pudgalavadin School, and four others that derived from it, the Dharmottariya, the Bhadrayaniya, the Sammitiya and the Shannagarika.
Since the date of the Buddhas death was probably in about 486 BCE or 368 BCE (according to which sources one follows), the rise of the Vatsiputriya school would have been in the early third century or toward the middle of the second century BCE.
The Vatsiputriya and a branch of the Sammitiya survived in India at least until the tenth century, but since the Pudgalavadin schools never spread to any great extent beyond the subcontinent, when Buddhism died out in India, the tradition of the Pudgalavada came to an end.
Vatsiputriya, having heard this, paid homage and left.
If you go to the Buddha, please tell him: "The Brahmacarin, Vatsiputriya, having practised the two ways, has now attained the learninglessness knowledge.
The bhiksu, Vatsiputriya, wanted us to report to you that, having now practised the two ways, he has attained the learninglessness knowledge and that, feeling grateful, he will now enter Nirvana."