Paper search is an important activity for researchers, typically involvingusing a query with description of a topic to find relevant papers. As researchdeepens, paper search requirements may become more flexible, sometimesinvolving specific details such as module configuration rather than beinglimited to coarse-grained topics. However, previous paper search systems areunable to meet these flexible-grained requirements, as these systems mainlycollect paper abstracts to construct index of corpus, which lack detailedinformation to support retrieval by finer-grained queries. In this work, wepropose PaperRegister, consisted of offline hierarchical indexing and onlineadaptive retrieval, transforming traditional abstract-based index intohierarchical index tree for paper search, thereby supporting queries atflexible granularity. Experiments on paper search tasks across a range ofgranularity demonstrate that PaperRegister achieves the state-of-the-artperformance, and particularly excels in fine-grained scenarios, highlightingthe good potential as an effective solution for flexible-grained paper searchin real-world applications. Code for this work is inhttps://github.com/Li-Z-Q/PaperRegister.