Allocating distributed data structures and managing allocation of a symmetric heap can include defining, using a processor, the symmetric heap. The symmetric heap includes a symmetric partition for each process of a partitioned global address space (PGAS) system. Each symmetric partition of the symmetric heap begins at a same starting virtual memory address and has a same global symmetric break. One process of a plurality of processes of the PGAS system is configured as an allocator process that controls allocation of blocks of memory for each symmetric partition of the symmetric heap. Using the processor executing the allocator process, isomorphic fragmentation among the symmetric partitions of the symmetric heap is maintained.