Disclosed is a carbon nano-tube dispersant comprising a highly branched polymer having a repeating unit represented by, for example, formula (12) or (13), wherein the highly branched polymer is produced by the polycondensation of a triarylamine compound and an aldehyde compound and/or a ketone compound in the presence of an acid catalyst. The carbon nano-tube dispersant enables the dispersion of CNTs in a medium such as an organic solvent until the CNTs are so decomposed as to have an individual size. (In the formula, Z1 and Z2 independently represent a hydrogen atom, a phenyl group, a thienyl group, or the like.)