The adaptive control of strictly decentralised adaptive control systems has been investigated in the past and it has been demonstrated that, under very general conditions, exact asymptotic tracking by the different subsystems can be achieved without any communication between them. Here, the problem is discussed when communication between the different subsystems is permitted. The problems considered range from totally decentralised control to totally centralised control with emphasis on partial communication. In all cases, the problems can be posed as ones related to the stability of switching systems. The principal theoretical contribution is the demonstration that the overall system is globally stable, resulting in exact asymptotic tracking by all the subsystems. Decoupling stability and performance issues permit the designer to focus on improving the behaviour of the overall system. The principal practical contribution is the demonstration that significant improvement in transient responses of the subsystems can be achieved with communication at relatively few instants of time.