Supporting information 1. Affiliation of 1H NMR spectrum for the polymer The radical addition-coupling reaction must be as the major route in the polymerization, or Xn,GPC could not be as high in Table 2, and gels could not be obtained. ①For acrylate-typed carbon radical, disproportionation, coupling termination reaction and chain transfer reaction may occur, we made an in-depth study in this section. From the 1H NMR spectra of the products it was found a very small amount of coupling reaction units in the polymers (Figure 1), but it could be negligible in the main reactions of the polymerization. There was not found any evidence of disproportionation reaction of the carbon radical at δ=5.5-6.5. The chain transfer reaction of alkoxy amine radical can not be ignored if the coupling reaction between carbon radical and alkoxy amine radical was restrained due to steric effect, as shown in Figure 2. Figure 1. Evidence of self coupling reaction of carbon radicals in polymerization in the 1 H NMR spectra. Reaction condition: rA = 2nA1/(3nMNP) = 1, cA1 = 0.008M, VTHF = 4 mL, nCu: nPMDETA=1: 1, 25 oC, 15h. nCu = x×3nA1, x = 48% (a) and 52% (b), respectively. ② Trace amount of NOH in the end The 1H NMR spectrum of the polymer after deuterium exchange is shown in Figure 2. The disappeared peak indicated that reactive hydrogen existed in the polymer. To exclude the possibility of NH and SH in the monomer or product, and end alkoxy amine radical may occur hydrogen abstraction reaction to generate NOH structure [1-4] if the coupling reaction between carbon radical and alkoxy amine radical was restrained due to steric effect, NOH structure was confirmed. Figure 2. Comparison of the 1H NMR spectra of the polymer prepared by A1 and MNP before (above) and after (below) deuterium exchange. ③Cyclic structure detected by ESI-MS Figure 3. (a) ESI-MS spectrum of the product (nA1: nMNP: nCu: nPMDETA = 1: 3: 15: 10, [A1] = 0.001 M, VTHF = 80 ml, 25 °C, 40 h); (b) The right pictures are simplified structures for cyclic oligomers. As shown in Figure 3(a), the ESI-MS spectrum of the polymer exhibites peaks at 882.3 and 1741.5, which were assigned to cyclic oligomers with structures shown in Figure 3(b), identified as the sodium adduct ions. The result reflected unavoidable cyclic reactions between polyfunctional groups. The left model represented two cycles, and the right model represented three cycles. 2. Selective degradation of ester group in the polymer. Degradation of ester group in the polymer could occur at a certain concentration of KOH/methanol without jeopardizing NO–C, as shown in Scheme 1. The R–OC(O)–R’ structure in polymer could be changed to R–OH and CH3OC(O)–R’, while NO–C in polymer was conserved. Scheme 1. Degradation mechanism of hyperbranched polystyrene. To determine the appropriate degradation condition, we established two model polymers, dimethyl 2,9-dibromodecanedioate-alt-MNP and 3-arm P(tert-butyl acrylate), which was synthesized by the tribromide and tert-butyl acrylate via ATRP. The ester appeared at the side chain of dimethyl 2,9-dibromodecanedioate-alt-MNP but at the backbone of the 3-arm PtBA. If the ester is broken, the Mn,GPC of dimethyl 2,9-dibromodecanedioate- alt-MNP is similar with the original value, but Mn,GPC of 3-arm PtBA will reduce to 1/3 of the original value. Under the proper condition, polymers were degraded. The results could be seen in Figure 4 and Table 1. Fig. 4 Comparisons of GPC curves of two model polymers before and after ester exchange degradations in certain condition (left, the employed polymer is MNP-alt-dimethyl 2,9-dibromodecanedioate; right, the employed polymer is 3-arm PtBA). Table 1. Results of degradation of ester group in the polymers. Run Mn,GPC (g/mol) PDI Time (h) MNP-alt-dimethyl 13200 1.78 0 2,9-dibromodecanedioate After methanolysis a 14800 1.50 21 3-arm PtBA 9800 1.07 0 a After methanolysis 3700 1.22 15 a The cleavage test condition: 25 mg polymer, 2 ml of methanol and 3 ml of THF, 0.2 ml of 0.1M KOH/methanol solvent were added to a 10 ml round-bottom flask, sealed by stopper, kept at 50 °C. The NO–C in the linear polymer could be conserved after ester exchange reaction for 21 h, the Mn,GPC values were similar to each other before and after degradation. But R–C(O)O-R’ was changed into R–C(O)O-CH3 because the Mn,GPC of the 3-arm PtBA reduced to 1/3 of the original value in Table 1. However, NO–C would be destroyed if the KOH concentration was above 0.1M, and the process took a much longer time if the concentration was below this threshold. References 1 A. F. B. Stefan, C. Grégory, L. G. Anton, Macromolecules 32, 8269(1999). 2 E. Drockenmuller, J. M. Catala, Macromolecules 35, 2461(2002). 3 A. K. Hoffmann, A. T. Henderson, J. Am. Chem. Soc. 83, 4671(1961). 4 L. Li, G. K. Hamer, M. K. Georges, Macromolecules 39, 9201(2006).