A material comprising a highly branched carbohydrate polymer, a polyalkylene glycol (or polyalkylene oxide) linked to the highly branched carbohydrate polymer, and a hydrophobic or amphiphilic group linked to the highly branched carbohydrate polymer and/or the polyalkylene glycol (or polyalkylene oxide), is described. Methods of making and using the material, as well as a soluble composition that contains the material and a hydrophobic solute compound, are also described.