This review summarizes the synthesis of irregular hyperbranched polymer grafts on various inorganic and organic substrates. The synthesis of these hyperbranched grafts are generally based on "graft on a graft" polymerizations and include diverse sorts of graft polymers. The "graft-on-a-graft" strategies discussed here include chemistry leading to the synthesis of hyperbranched poly(acrylic acid) grafts, polysiloxane grafts, dendrimer/polyanhydride graft nanocomposites, ring-opening polymerization grafts, and polyamidoamine grafts. Other relevant chemistry of these grafts including chemistry leading to derivatives of hyperbranched poly(acrylic acid) grafts, further modification by polyionic interactions, polyvalent hydrogen bonding, and functional group manipulation is discussed. Examples of reactions of monomers with polyvalent surfaces that lead to hyperbranched grafts are also briefly discussed.

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