A method for the production of a population of expanded activated NK cells, comprising: producing a population of cells containing NK cells from at least n UCB units, or fraction thereof containing said NK cells, by a method comprising the steps of: (a) providing at least n umbilical cord blood units (UCB units), or fraction thereof containing said cells, with n ≥ 2, and (b) pooling said at least n UCB units, or fraction thereof containing said cells, to produce the population of cells expanding and activating said NK cells obtained from the step in a suitable medium to produce said population of expanded activated NK cells; and recovering said expanded activated NK cells, wherein said method comprising in step, - a step (c) of depleting T cells from said population of cells obtained in (b), or - a step of depleting T cells contained in each of said n UCB units before the step (b) of pooling said UCB units, wherein said n UCB units when pooled present the same pattern for major HLA class I groups genotypes and wherein said major HLA class I group is selected from the group consisting of HLA A3/A11 which is recognized by KIR3DL2, HLA Bw4 which is recognized by KIR3DL1, HLA C group 1 which is recognized by KIR2DL2/3, and HLA C group 2 which is recognized by KIR2DL; and wherein the suitable medium to expand and to activate the NK cells in step comprises accessory cells, said accessory cells and the NK cells to be expanded and activated being HLA-KIR mismatched. producing a population of cells containing NK cells from at least n UCB units, or fraction thereof containing said NK cells, by a method comprising the steps of: (a) providing at least n umbilical cord blood units (UCB units), or fraction thereof containing said cells, with n ≥ 2, and (b) pooling said at least n UCB units, or fraction thereof containing said cells, to produce the population of cells (a) providing at least n umbilical cord blood units (UCB units), or fraction thereof containing said cells, with n ≥ 2, and (b) pooling said at least n UCB units, or fraction thereof containing said cells, to produce the population of cells expanding and activating said NK cells obtained from the step in a suitable medium to produce said population of expanded activated NK cells; and recovering said expanded activated NK cells, wherein said method comprising in step, - a step (c) of depleting T cells from said population of cells obtained in (b), or - a step of depleting T cells contained in each of said n UCB units before the step (b) of pooling said UCB units, wherein said n UCB units when pooled present the same pattern for major HLA class I groups genotypes and wherein said major HLA class I group is selected from the group consisting of HLA A3/A11 which is recognized by KIR3DL2, HLA Bw4 which is recognized by KIR3DL1, HLA C group 1 which is recognized by KIR2DL2/3, and HLA C group 2 which is recognized by KIR2DL; and wherein the suitable medium to expand and to activate the NK cells in step comprises accessory cells, said accessory cells and the NK cells to be expanded and activated being HLA-KIR mismatched. - a step (c) of depleting T cells from said population of cells obtained in (b), or - a step of depleting T cells contained in each of said n UCB units before the step (b) of pooling said UCB units,