We introduce AdaCoSeg, a deep neural network architecture for adaptive co-segmentation of a set of 3D shapes represented as point clouds. Differently from the familiar single-instance segmentation problem, co-segmentation is intrinsically contextual: how a shape is segmented can vary depending on the set it is in. Hence, our network features an adaptive learning module to produce a consistent shape segmentation which adapts to a set. Specifically, given an input set of unsegmented shapes, we first employ an offline pre-trained part prior network to propose per-shape parts. Then, the co-segmentation network iteratively and jointly optimizes the part labelings across the set subjected to a novel group consistency loss defined by matrix ranks. While the part prior network can be trained with noisy and inconsistently segmented shapes, the final output of AdaCoSeg is a consistent part labeling for the input set, with each shape segmented into up to (a user-specified) K parts. Overall, our method is weakly supervised, producing segmentations tailored to the test set, without consistent ground-truth segmentations. We show qualitative and quantitative results from AdaCoSeg and evaluate it via ablation studies and comparisons to state-of-the-art co-segmentation methods.