Space Complexity

You store the original tree ($O(n)$ space for adjacency lists) and the decomposition tree ($O(n)$ space for parent pointers). Distance arrays during DFS use $O(n)$ space. If you store distances from every centroid to all nodes (for distance queries), that is $O(n \log n)$ space because each node appears in $O(\log n)$ centroid subtrees.

For most problems, $O(n \log n)$ space is acceptable with modern memory limits. If space is tight, recompute distances on-the-fly instead of storing them.