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.