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Unsupervised domain adaptation (UDA) has been a vital protocol for migrating information learned from a labeled source domain to facilitate the implementation in an unlabeled heterogeneous target domain. Although UDA is typically jointly trained on data from both domains, accessing the labeled source domain data is often restricted, due to concerns over patient data privacy or intellectual property. To sidestep this, we propose "off-the-shelf (OS)" UDA (OSUDA), aimed at image segmentation, by adapting an OS segmentor trained in a source domain to a target domain, in the absence of source domain data in adaptation. Toward this goal, we aim to develop a novel batch-wise normalization (BN) statistics adaptation framework. In particular, we gradually adapt the domain-specific low-order BN statistics, e.g., mean and variance, through an exponential momentum decay strategy, while explicitly enforcing the consistency of the domain shareable high-order BN statistics, e.g., scaling and shifting factors, via our optimization objective. We also adaptively quantify the channel-wise transferability to gauge the importance of each channel, via both low-order statistics divergence and a scaling factor.~Furthermore, we incorporate unsupervised self-entropy minimization into our framework to boost performance alongside a novel queued, memory-consistent self-training strategy to utilize the reliable pseudo label for stable and efficient unsupervised adaptation. We evaluated our OSUDA-based framework on both cross-modality and cross-subtype brain tumor segmentation and cardiac MR to CT segmentation tasks. Our experimental results showed that our memory consistent OSUDA performs better than existing source-relaxed UDA methods and yields similar performance to UDA methods with source data.