Convex splitting is a powerful tool in quantum information theory that are widely used in many information-processing protocols such as quantum state distribution and quantum channel coding. In this talk, I will present some near optimal one-shot estimates for convex splitting using noncommutative $L_p$-spaces. This yields error and strong converse exponent estimate as well as matched second-order asymptotics. Moreover, our error exponent estimate also applies to multipartite case, which leads to the resolution of Quantum Broadcast Channel Simulation. This talk is based on joint works with Hao-Chung Cheng and Mario Berta.