polymerization of monomers having those groups or by post modification of the hyperbranched polymer via known chemical reactions examples of hyperbranched polymers having hydrophilic end groups useful in the invention include a hyperbranched polyamide with both amine and carboxylic acid end groups a hyperbranched polyamide with carboxylic acid end groups a hyperbranched polyamide with amine end groups a hyperbranched polyamide with quaternized end groups a hyperbranched aliphatic polyester with hydroxy end groups a hyperbranched aliphatic polyester with carboxylic acid end groups a hyperbranched aliphatic polyester with combined hydroxy and carboxylic acid end groups a hyperbranched aromatic polyester with carboxylic acid end groups a hyperbranched aromatic polyester with sulfonic acid end groups a hyperbranched polyether with hydroxy end groups a hyperbranched quaterized poly chloromethyl styrene a hyperbranched poly vinyl benzene sulfonyl chloride with sulfonic acid end groups a hyperbranched polyesteramide with hydroxy end groups a hyperbranched polyesteramide with carboxylic acid end groups a hyperbranched polyesteramide with combined hydroxy and carboxylic acid end groups a hyperbranched polyesteramide with quaternized end groups or a hyperbranched polyesteramide with combined hydroxy and quaterized end groups in another preferred embodiment of the invention the hyperbranched polymer having hydrophilic end groups can be added as an additive together with a pigment dispersion to prepare the ink in another preferred embodiment of the invention the hyperbranched polymer having hydrophilic end groups can be used as a dispersant to disperse the pigment particles used in ink.