Aqueous pigment dispersions, and using

The present invention comprises at least a pigment, water, a polymeric dispersing agent, and an alkali, the polymer dispersant is in the General Formula 1] diblock polymer A-B or [Formula 2] A- a B-C triblock polymers, these block polymers, the organic iodide and a polymerization initiator compound, an organic phosphorus compound, an organic nitrogen compound or an organic oxygen compound as a catalyst, an addition polymerizable monomer with a radical generator aqueous pigment dispersion which is a block polymer obtained by polymerization, its preparation and use. According to the present invention, problems of the conventional living radical polymerization can be obtained by easy living radical polymerization methods do not, by molecules precisely controlled polymeric dispersant, the aqueous pigment dispersion in which a pigment is dispersed with it is possible to provide.