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We investigate the complexity of performing updates on probabilistic XML data for various classes of probabilistic XML documents of different succinctness. We consider two elementary kinds of updates, insertions and deletions, that are defined with the help of a locator query that specifies the nodes where the update is to be performed. For insertions, two semantics are considered, depending on whether a node is to be inserted once or for every match of the query. We first discuss deterministic updates over probabilistic XML, and then extend the algorithms and complexity bounds to probabilistic updates. In addition to a number of intractability results, our main result is an efficient algorithm for insertions defined with branching-free queries over probabilistic models with local dependencies. Finally, we discuss the problem of updating probabilistic XML databases with continuous probability distributions.