Complex amphiphilic polymer architectures have very different self-assembly properties to their linear counterparts. Miktoarm stars have been the most studied in this regard but their synthesis is usually complex with many synthetic steps. Moreover, there are few examples of building 3-arms stars with cyclic building blocks. In this work, we have demonstrated the rapid (in 30 min) and highly efficient (at close to 99%) one-pot synthesis of mikto 3-arm AB(2) star at 25 degrees C using two copper catalyzed "click"-type reactions (i.e., CuAAC and nitroxide radical coupling, NRC). By modulating the copper activity, the rates of NRC and CuAAC could be significantly changed. Under conditions where both the NRC and CuAAC reactions were similar, well-defined linear and cyclic building blocks consisting of linear-polystyrene, cyclic-polystyrene, poly(tert-butyl acrylate) and PEG could be combined to form a wide variety of chemically different AB(2) stars. The log-normal distribution (LND) method was used to simulate the molecular weight distribution using experimental M-n, PDI and change in hydrodynamic volumes, and this method provided an additional and sensitive characterization method to the coupling efficiency for 3-arm formation. It allowed the determination of the type and amount of starting, two-arm or other high molecular weight species present after coupling. There were no adjustable parameters used in the LND simulations, making this a powerful method to characterize not only cyclic polymers but more complex architectures like 3-arm stars with very different chemical compositions. The LND simulations gave excellent agreement with the experimental MWDs, allowing us to determine the coupling efficiency of greater than 99% in most cases.