A method, apparatus, and system for hierarchical organization of tablespace free space metadata in a database are provided. The hierarchy is divided into at least two levels: level 1 or L1 bitmap blocks are stored as a shared data structure and map free space in a tablespace, whereas level 2 or L2 bitmap blocks are stored as separate local copies at each database instance and map to the L1 bitmap blocks. This hierarchical organization provides a mechanism for finer grained concurrency control, enabling highly parallel tablespace metadata processing to accommodate the performance requirements of large tablespaces with big data sets. By integrating the hierarchical organization as part of the tablespace stack layer in a database management system (DBMS), implementations can be provided transparently to database end users without demanding any additional administrative, maintenance, or development burdens.