Binary Partition Hierarchies (BPHs) and Minimum Spanning Trees are key structures in hierarchical image analysis. However, the explosion in the size of image data poses a new challenge, as the memory available in conventional workstations becomes insufficient to execute classical algorithms. To address this problem, specific algorithms have been proposed for out-of-core computation of BPHs, where a BPH is actually represented by a collection of smaller trees, called a distribution, thus reducing the memory footprint of the algorithms. In this article, we address the problem of designing efficient out-of-core algorithms for computing classical attributes in distributions of BPHs, which is a necessary step towards a complete out-of-core hierarchical analysis workflow that includes tasks such as connected filtering and the generation of other representations such as hierarchical watersheds. The proposed algorithms are based on generic operations designed to propagate information through the distribution of trees, enabling the computation of attributes such as area, volume, height, minima and number of minima.