A block polymer comprised of a polyalkenyl ether main chain comprises a first block segment having hydrophobicity; a second block segment having an upper limit hydration temperature exceeding 70.degree. C.; and a third block segment having an ionic property. A polymer-containing composition comprises the block polymer, a solvent or a dispersing medium, and a functional substance. An ink composition comprises the polymer-containing composition wherein the functional substance is colorant. A liquid application method comprises the steps of preparing the polymer-containing composition; and applying the polymer-containing composition to a medium. A liquid application apparatus comprises a liquid application means which makes energy act on the polymer-containing composition to apply the composition; and a drive means which drives the liquid application means. The polymer compound is capable of satisfactorily dispersing a functional substance in a solvent.