Implementations relate to interactions, over a wireless communication modality, between an automated assistant of an automobile computer system, and separate client device(s). In some of those implementations, the client device(s) can be paired with the automobile computer system, and the client device(s) and the automobile computer system can include separate instances of an automated assistant, which can be associated with different user accounts. In some additional or alternative implementations, particular actions to be performed by a local application of a client device can be advanced via user interaction with the automobile automated assistant, despite a counterpart to the local application not being installed directly on automobile computer system. For example, despite an automobile computer system not having a third-party messaging application installed, the automobile automated assistant can access requested actions to be performed by the third-party messaging application in order to further a requested action. The automobile computer system can transmit, via the wireless communication modality, content to cause the third-party application to further the requested action.