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Low-dimensional narrow-band-gap III-V semiconductors are key building blocks for the next generation of high-performance nanoelectronics, nanophotonics, and quantum devices. Realizing these various applications requires an efficient methodology that enables the material dimensional control during the synthesis process and the mass production of these materials with perfect crystallinity, reproducibility, low cost, and outstanding electronic and optoelectronic properties. Although advances in one- and two-dimensional narrow-band-gap III-V semiconductors synthesis, the progress toward reliable methods that can satisfy all of these requirements has been limited. Here, we demonstrate an approach that provides a precise control of the dimension of InAs from one-dimensional nanowires to wafer-scale free-standing two-dimensional nanosheets, which have a high degree of crystallinity and outstanding electrical and optical properties, using molecular-beam epitaxy by controlling catalyst alloy segregation. In our approach, two-dimensional InAs nanosheets can be obtained directly from one-dimensional InAs nanowires by silver-indium alloy segregation, which is much easier than the previously reported methods, such as the traditional buffering technique and select-area epitaxial growth. Detailed transmission electron microscopy investigations provide solid evidence that the catalyst alloy segregation is the origination of the InAs dimensional transformation from one-dimensional nanowires to two-dimensional nanosheets and even to three-dimensional complex crosses. Using this method, we find that the wafer-scale free-standing InAs nanosheets can be grown on various substrates including Si, MgO, sapphire, GaAs, etc. The InAs nanosheets grown at high temperature are pure-phase single crystals and have a high electron mobility and a long time-resolved terahertz kinetics lifetime. Our work will open up a conceptually new and general technology route toward the effective controlling of the dimension of the low-dimensional III-V semiconductors. It may also enable the low-cost fabrication of free-standing nanosheet-based devices on an industrial scale.