Nickel-cobalt-manganese complex hydroxide particles and method for producing same, positive electrode active material for nonaqueous electrolyte secondary battery and method for producing same, and nonaqueous electrolyte second battery

A method for producing a nickel cobalt manganese composite hydroxide by a crystallization reaction is provided. The method includes: a nucleation step of performing nucleation by controlling a pH of an aqueous solution for nucleation including metal compounds containing nickel, cobalt and manganese, and an ammonium ion donor to 12.0 to 14.0 in terms of the pH as measured at a liquid temperature of 25° C. as a standard; and a particle growth step of growing nuclei by controlling a pH of an aqueous solution for particle growth containing nuclei formed in the nucleation step to 10.5 to 12.0 in terms of the pH as measured at a liquid temperature of 25° C. as a standard.