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The adaptation of a Generative Adversarial Network (GAN) aims to transfer a pre-trained GAN to a target domain with limited training data. In this paper, we focus on the one-shot case, which is more challenging and rarely explored in previous works. We consider that the adaptation from a source domain to a target domain can be decoupled into two parts: the transfer of global style like texture and color, and the emergence of new entities that do not belong to the source domain. While previous works mainly focus on style transfer, we propose a novel and concise framework to address the \textit{generalized one-shot adaptation} task for both style and entity transfer, in which a reference image and its binary entity mask are provided. Our core idea is to constrain the gap between the internal distributions of the reference and syntheses by sliced Wasserstein distance. To better achieve it, style fixation is used at first to roughly obtain the exemplary style, and an auxiliary network is introduced to the generator to disentangle entity and style transfer. Besides, to realize cross-domain correspondence, we propose the variational Laplacian regularization to constrain the smoothness of the adapted generator. Both quantitative and qualitative experiments demonstrate the effectiveness of our method in various scenarios. Code is available at \url{https://github.com/zhangzc21/Generalized-One-shot-GAN-adaptation}.