Sautrāntika 經量部, like other Buddhist traditions, defends the doctrines of karma and reincarnation. Unlike the Vātsīputrīyas 犢子部, who regard the pudgala 補特伽羅 or individual person as the bearer of karma from one life to the next, Sautrāntika rejects the notion that the pudgala serves as the stable bearer of karma, on the grounds that it violates the Buddhist doctrine of momentariness 刹那滅. Even though they reject the pudgala, Sautrāntika scholars such as Śrīlāta 室利邏多 deploy the theory of the subsidiary element or *anudhātu to reject the realist doctrine of a mind-independent reality. For Sautrāntika, the collection of subsidiary elements pursuant upon the mind serves as the locus of transmigration from one life to the next. The postulate of dharmas external to the mind is not needed to explain the continuity of mental processes. The accumulation of subsidiary elements in the mind means that one does not need an unchanging substratum to account for direct and indirect causal efficacy in the face of radical momentariness.

References:

Cox, Collett. 1995. Disputed Dharmas: Early Buddhist Theories on Existence with an Annotated Translation of the Section on Factors Dissociated from Thought from Saṃghabhadraʼs Nyāyānusāra. Tokyo:  InternationalInstitute of Buddhist Studies.

Mitomo, Kenyō . 1980. “Kyū zuikai ni tsuite 舊隨界說について .” Indogaku Bukkyōgaku kenkyū 29 (1): 25–30.

Mizuno, Kōgen 水野弘元. Shi, Huimin, trans. 1994. Fojiao jiaoli yanjiu 佛教教理硏究：水野弘元著作選集，. Taipei:  Zhonghua Foxue yanjiu suo luncong. vol. 2