## 1 Introduction  
[PERSON] investigated that the physical properties of polymers and, accordingly, their practical applications would be related to their macromolecular topologies [1, 2]. After the first reported syntheses of dendrimers, intense research efforts were dedicated toward finding new and simpler approaches for the formation of highly branched macromolecules [3, 4]. Both convergent and divergent methods have been used to synthesize numerous examples of dendrimers with compositionally and functionally tunable inner and outer region and unique globular shapes [5, 6, 7]. In addition, approximations to the regular structures of dendrimers have been accomplished through the synthesis of hyperbranched polymers. Although the structures of hyperbranched polymers are less regular than those of dendrimers, they may be more conducive to industrial applications because of their simpler syntheses. In early syntheses of hyperbranched polymers, reactions of monomers AB\(x\) (\(x\geq 2\)) where the A and B groups can condense with each other exclusively resulted in step-growth polymerization becoming a predominant method. Thus, an enormous numbers of different types of hyperbranched polymers have been synthesized, including polyphenylenes [8, 9], polyesters [10, 11, 12], polyether [13, 14], polysiloxysilanes [15], and polybenzamides [16, 17], a variety of which have been reviewed [18, 19]. Through conventional step-growth mechanisms, hyperbranched polymers can be synthesized in one-pot, avoiding the need for multiple reactions with protection, deprotection, and purification steps typically required for constructing perfect dendrimers, but with the drawback of large polydispersities in molecular weight and structure. Recent developments in chain-growth condensation polymerization (CGCP, an analogue to living condensation polymerization), have allowed the syntheses of hyperbranched aromatic polyamides having high degrees of polymerization and very narrow molecular weight distributions (\(D\leq 1.13\)) through simple condensation polymerization of special AB\({}_{2}\) monomers [20, 21, 22]. The enormous efforts aimed at developing living chain-growth polymerizations on developments of branched structures (e.g., cationic [23]/anionic [24, 25] polymerization, nitroxide-mediated radical polymerization (NMRP) [26, 27], atom transfer radical polymerization (ATRP) [28, 29, 30, 31], group transfer polymerization (GTP) [32, 33], UV-initiated RAFT (reversible addition-fragmentation chain-transfer) polymerization [34, 35], and ring-opening (metathesis) polymerization (RO(M)P) [36, 37]), have led to many novel systems being amenable to the syntheses of hyperbranched polymers. One of the most promising approaches is the synthesis of hyperbranched polymers through atom transfer radical self-condensing vinyl polymerization (AT-SCVP) of AB* inimers [28, 29, 38]. Scheme 1 presents a typical mechanism for AT-SCVP used to prepare hyperbranched polymers. The AB*-type inimer, featuring both initiation and propagation sites, can be activated externally (e.g., using Cu(I)/L (L: ligand)). Because the initiation and the propagation sites have similar reactivities, chain propagation and re-initiation proceed simultaneously, leading to a polymer topology having a hyperbranched structure. As mentioned above, SCVP approaches with AB*-type inimers have been applied widely to NMRP, GTP, RO(M)P, and cationic/anionic polymerizations. **Scheme 1. ** General mechanism of atom transfer self-condensing vinyl polymerization (AT-SCVP) of an AB*-type inimer. Specifically, the concept of \"active site transfer\" has attracted interests for the synthesis of hyperbranched structures; it involves switching the active site within intra-propagating chains or among inter-propagating chains during the periods of initiation and propagation to control the polymer topology. One approach is to use \"iniferter\" monomers containing a chain-transfer group (e.g., methacrylate and styrene derivatives with a dithioester [39] or thiocarbamate [35,40] groups).