The emergence of Distributed Ledger Technologies and Cryptocurrencies impacts on how transactions of various assets between parties in highly dynamical settings – such as the Internet of Things or Smart Cities – are modelled and implemented in several ways. We study this transition from centralized accounts with explicit owners towards distributed ledgers with challenge-based transaction access control. We capture the transition in a series of linked formal specifications in Z, enabling the comparison between the two settings. In particular, we provide a reference model and then refine it for the respective settings.