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The reaction of $AB_m$ monomers (m=2,3) with a multifunctional B_f-typepolymer chain ("hypergrafting") is studied by coarse-grained molecular dynamicssimulations. The $AB_m$ monomers are hypergrafted using the slow monomeraddition strategy. Fully dendronized, i.e., perfectly branched polymers arealso simulated for comparison. The degree of branching DB of the moleculesobtained with the "hypergrafting" process critically depends on the rate withwhich monomers attach to inner monomers compared to terminal monomers. Thisratio is more favorable if the $AB_m$ monomers have lower reactivity, since thefree monomers then have time to diffuse inside the chain. Configurational chainproperties are also determined, showing that the stretching of the polymerbackbone as a consequence of the "hypergrafting" procedure is much lesspronounced than for perfectly dendronized chains. Furthermore, we analyze thescaling of various quantities with molecular weight M for large M (M>100). TheWiener index scales as $M^2.3$, which is intermediate between linear chains($M^3$) and perfectly branched polymers ($M^2 \ln(M)$). The polymer size,characterized by the radius of gyration $R_g$ or the hydrodynamic radius $R_h$,is found to scale as $R_{g,h}~M^{\nu}$ with $\nu~0.38$, which lies between theexponent of diffusion limited aggregation ($\nu=0.4$) and the mean-fieldexponent predicted by Konkolewicz and coworkers ($\nu=0.33$).

Statistical properties of linear-hyperbranched graft copolymers prepared  via "hypergrafting" of AB_m monomers from linear B-functional core chains: A  Molecular Dynamics simulation