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Temporal networks are essential for modeling and understanding systems whose behavior varies in time, from social interactions to biological systems. Often, however, real-world data are prohibitively expensive to collect in a large scale or unshareable due to privacy concerns. A promising way to bypass the problem consists in generating arbitrarily large and anonymized synthetic graphs with the properties of real-world networks, namely `surrogate networks'. Until now, the generation of realistic surrogate temporal networks has remained an open problem, due to the difficulty of capturing both the temporal and topological properties of the input network, as well as their correlations, in a scalable model. Here, we propose a novel and simple method for generating surrogate temporal networks. Our method decomposes the input network into star-like structures evolving in time. Then those structures are used as building blocks to generate a surrogate temporal network. Our model vastly outperforms current methods across multiple examples of temporal networks in terms of both topological and dynamical similarity. We further show that beyond generating realistic interaction patterns, our method is able to capture intrinsic temporal periodicity of temporal networks, all with an execution time lower than competing methods by multiple orders of magnitude. The simplicity of our algorithm makes it easily interpretable, extendable and algorithmically scalable.