We introduce the PaintNet dataset to accelerate research on supervised learning for multi-path prediction conditioned on free-shape 3D objects. PaintNet includes more than 800 object meshes and the associated spray painting strokes collected in a real industrial setting. The data currently covers four object categories of growing complexity: cuboids, windows, shelves, containers. All object meshes are already provided in a subdivided, smoothed watertight version to avoid sharp edges and holes. For each object, the associated unordered set of spray painting paths (a.k.a. strokes) is given, each being a sequence of end-effector poses. The 6-dimensional poses encode the 3D position of the ideal paint deposit point—12cm away from the gun nozzle—and the gun orientations as Euler angles. Each pose is collected by sampling from the end-effector kinematics at a rate of 4ms during offline program execution.