We present a distributed, event-triggered, and adaptive control algorithm for cooperative object manipulation withrolling contacts and unknown dynamic parameters. Whereasconventional cooperative manipulation methods require rigidcontact points, our approach exploits rolling effects of passiveend-effectors and does not require force/torque sensing. Theremoval of rigidity allows for more modular grasping, increasedapplication to more object types, and online adjustment ofthe grasp. The proposed control algorithm exhibits the following properties. Firstly, it is distributed, in the sense thatthe robotic agents calculate their own control signal, under anevent-triggered communication scheme. Such a scheme reducesthe inter-agent communication requirements with respect tocontinuous communication schemes. Secondly, it uses an onlineadaptation mechanism to accommodate for unknown dynamicparameters of the object and the agents. Finally, it adaptsexisting internal force controllers to guarantee no slip throughoutthe manipulation task despite the event-triggered nature of thecommunication scheme. Hardware implementation validates theeffectiveness of the proposed approach.