We cast segmentation of 3D tubular structures in a bundle as partitioning of structural-flow trajectories. Traditional 3D segmentation algorithms aggregate local pixel correlations incrementally along a 3D stack. In contrast, structural-flow trajectories establish long range pixel correspondences and their affinities propagate grouping cues across the entire volume simultaneously, from informative to non-informative places. Segmentation by trajectory clustring recovers from persistent ambiguities caused by faint boundaries or low contrast, common in medical images. Trajectories are computed by linking successive registration fields, each one registering pairs of consecutive slices of the 3D stack. We show our method effectively unravels densely packed tubular structures, without any supervision or 3D shape priors, outperforming previous 2D and 3D segmentation algorithms.