The solution of partial differential equations on a parallel computer is usually done by a data parallel approach. The grid is partitioned and mapped onto the processors. However, partitioning of unstructured meshes and adaptively refined meshes in general is an NP-hard problem and heuristics are needed. In this paper a parallelisable and cheap method based on space-filling curves is analysed. Quasi-optimal estimates are derived for partitions of adaptively refined grids.