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Despite impressive progress in object detection over the last years, it is still an open challenge to reliably detect objects across visual domains. Although the topic has attracted attention recently, current approaches all rely on the ability to access a sizable amount of target data for use at training time. This is a heavy assumption, as often it is not possible to anticipate the domain where a detector will be used, nor to access it in advance for data acquisition. Consider for instance the task of monitoring image feeds from social media: as every image is created and uploaded by a different user it belongs to a different target domain that is impossible to foresee during training. This paper addresses this setting, presenting an object detection algorithm able to perform unsupervised adaption across domains by using only one target sample, seen at test time. We achieve this by introducing a multi-task architecture that one-shot adapts to any incoming sample by iteratively solving a self-supervised task on it. We further enhance this auxiliary adaptation with cross-task pseudo-labeling. A thorough benchmark analysis against the most recent cross-domain detection methods and a detailed ablation study show the advantage of our method, which sets the state-of-the-art in the defined one-shot scenario.