Providing distributed processes with concurrent objects is a fundamental service that has to be offered by any distributed system. The classical shared read/write register is one of the most basic ones. Several protocols have been proposed that build an atomic register on top of an asynchronous messagepassing system prone to process crashes. In the same spirit, this paper addresses the implementation of a regular register (a weakened form of an atomic register) in an asynchronous dynamic message-passing system. The aim is here to cope with the net effect of the adversaries that are asynchrony and dynamicity (the fact that processes can enter and leave the system). The paper focuses on the class of dynamic systems the churn rate c of which is constant. It presents two protocols, one applicable to synchronous dynamic message passing systems, the other one to asynchronous dynamic systems. Both protocols rely on an appropriate broadcast communication service (similar to a reliable brodcast). Each requires a specific constraint on the churn rate c. Both protocols are first presented in an as intuitive as possible way, and are then proved correct.