This paper presents a new algorithm for the fast, shared memory multi-threaded computation of contour trees on tetrahedral meshes. In contrast to previous multi-threaded algorithms, our technique computes the augmented contour tree. Such an augmentation is required to enable the full extent of contour tree based applications, including for instance data segmentation. Our approach relies on a range-driven domain partitioning. We show how to exploit such a partitioning to rapidly compute contour forests. We also show how such forests can be efficiently turned into the output contour tree. We report performance numbers that compare our approach to a reference sequential implementation for the computation of augmented contour trees. These experiments demonstrate the run-time efficiency of our approach. We demonstrate the utility of our approach with several data segmentation tasks. We also provide a lightweight VTK-based C++ implementation of our approach for reproduction purposes.