Implementations are directed to dynamically adapting which assistant on-device model(s) are locally stored at assistant devices of an assistant device group and/or dynamically adapting the assistant processing role(s) of the assistant device(s) of the assistant device group. In some of those implementations, the corresponding on-device model(s) and/or corresponding processing role(s), for each of the assistant devices of the group, is determined based on collectively considering individual processing capabilities of the assistant devices of the group. Implementations are additionally or alternatively directed to cooperatively utilizing assistant devices of a group, and their associated post-adaptation on-device model(s) and/or post-adaptation processing role(s), in cooperatively processing assistant requests that are directed to any one of the assistant devices of the group.