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Context. New-generation cosmological simulations are providing huge amounts of data, whose analysis becomes itself a cutting-edge computational problem. In particular, the identification of gravitationally bound structures, known as halo finding, is one of the main analyses. A handful of codes developed to tackle this task have been presented during the last years. Aims. We present a deep revision of the already existing code ASOHF. The algorithm has been throughfully redesigned in order to improve its capabilities to find bound structures and substructures, both using dark matter particles and stars, its parallel performance, and its abilities to handle simulation outputs with vast amounts of particles. This upgraded version of ASOHF is conceived to be a publicly available tool. Methods. A battery of idealised and realistic tests are presented in order to assess the performance of the new version of the halo finder. Results. In the idealised tests, ASOHF produces excellent results, being able to find virtually all the structures and substructures placed within the computational domain. When applied to realistic data from simulations, the performance of our finder is fully consistent with the results from other commonly used halo finders, with remarkable performance in substructure detection. Besides, ASOHF turns out to be extremely efficient in terms of computational cost. Conclusions. We present a public, deeply revised version of the ASOHF halo finder. The new version of the code produces remarkable results finding haloes and subhaloes in cosmological simulations, with an excellent parallel performance and with a contained computational cost.