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The prowess that makes few-shot learning desirable in medical image analysis is the efficient use of the support image data, which are labelled to classify or segment new classes, a task that otherwise requires substantially more training images and expert annotations. This work describes a fully 3D prototypical few-shot segmentation algorithm, such that the trained networks can be effectively adapted to clinically interesting structures that are absent in training, using only a few labelled images from a different institute. First, to compensate for the widely recognised spatial variability between institutions in episodic adaptation of novel classes, a novel spatial registration mechanism is integrated into prototypical learning, consisting of a segmentation head and an spatial alignment module. Second, to assist the training with observed imperfect alignment, support mask conditioning module is proposed to further utilise the annotation available from the support images. Extensive experiments are presented in an application of segmenting eight anatomical structures important for interventional planning, using a data set of 589 pelvic T2-weighted MR images, acquired at seven institutes. The results demonstrate the efficacy in each of the 3D formulation, the spatial registration, and the support mask conditioning, all of which made positive contributions independently or collectively. Compared with the previously proposed 2D alternatives, the few-shot segmentation performance was improved with statistical significance, regardless whether the support data come from the same or different institutes.