Parallelization is one of the most effective blockchain scalability solutions, and the existing parallelization schemes can be classified into two categories, i.e., starlike structure and parallel structure, according to the network structure. However, the current research lacks the analyses of factors affecting the performance boundary and performance bottleneck in starlike sharding structure. To address this problem, this study abstracts a general starlike sharding structure of blockchains for the schemes adopting different starlike sharding structure, and the transaction process in this general structure is quantitatively modeled to derive the relationship between throughput and the number of shards in starlike sharding structure. According to the constructed model, there exists a performance limit in starlike sharding structure and an optimal sharding quantity to maximize the system throughput. An explicit functional relationship exists between the maximal throughput and the functional complexity of the mainchain. With the proposed throughput model, related blockchain systems can balance the number of shards and the functional complexity of the mainchain to reach the theoretical upper limit of system throughput with the consideration of their specific design. Therefore, the work of this study has significant guiding value in the design of the schemes adopting starlike parallelization.