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We investigate rifting during continental collision in southern Tibet by testing kinematic models for two classes of rifts: Tibetan rifts are defined as >150 km in length and crosscut the Lhasa Terrane, and Gangdese rifts are <150 km long and isolated within the high topography of the Gangdese Range. Discerning rift kinematics is a crucial step towards understanding rift behavior and evolution that has been historically limited. We evaluate spatiotemporal trends in fault displacement and extension onset in the Tangra Yumco (TYC) rift and several nearby Gangdese rifts and examine how contraction and rift exhumation relate to evolution of the Gangdese drainage divide. Igneous U-Pb and zircon (U-Th)/He (ZHe) results indicate rift footwall crystallization between ~59-49 Ma and cooling between ~60-4 Ma, respectively, with ZHe ages correlating with sample latitude. Samples from Gangdese latitudes (~29.4-29.8°N) yield predominantly Oligocene-early Miocene ages, whereas samples north of ~29.8°N yield both late Miocene-Pliocene ages and Paleocene-Eocene ages. Thermal history models indicate two-stage cooling, with initially slow cooling followed by accelerated cooling during late Miocene-Pliocene time. From spatial distributions of ZHe ages we interpret: (1) ~28-16 Ma ages from Gangdese latitudes reflect exhumation along contractional structures, (2) ~8-4 Ma ages reflect rift-related exhumation, and (3) ~60-48 Ma ages indicate these samples experienced lesser rift exhumation. Our data are consistent with a segment linkage evolution model for the TYC rift, with interactions between rifts and contractional structures likely influencing the evolution of topography and location of the Gangdese drainage divide since Miocene time