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Task-oriented dialog systems rely on dialog state tracking (DST) to monitor the user's goal during the course of an interaction. Multi-domain and open-vocabulary settings complicate the task considerably and demand scalable solutions. In this paper we present a new approach to DST which makes use of various copy mechanisms to fill slots with values. Our model has no need to maintain a list of candidate values. Instead, all values are extracted from the dialog context on-the-fly. A slot is filled by one of three copy mechanisms: (1) Span prediction may extract values directly from the user input; (2) a value may be copied from a system inform memory that keeps track of the system's inform operations; (3) a value may be copied over from a different slot that is already contained in the dialog state to resolve coreferences within and across domains. Our approach combines the advantages of span-based slot filling methods with memory methods to avoid the use of value picklists altogether. We argue that our strategy simplifies the DST task while at the same time achieving state of the art performance on various popular evaluation sets including Multiwoz 2.1, where we achieve a joint goal accuracy beyond 55%.