Rapid solidification of bulk Ag42.4Cu21.6Sb36 ternary eutectic alloy is accomplished by glass fluxing method, during which the maximum undercooling attains 114 K (0.16TE). Under high undercooling conditions, the ternary eutectic consists of ε(Ag3Sb), (Sb) and θ(Cu2Sb) phases, instead of (Ag), (Sb) and θ phases as predicted by the phase diagram. In the sample of small undercooling, the alloy microstructure is characterized by the mixture of primary θ(Cu2Sb), (ε+θ) and (ε+Sb) pseudobinary eutectics, and regular (ε+θ+Sb) ternary eutectic. With the increase of undercooling,θ(Cu2Sb) primary phase and pseudobinary eutectics disappear gradually, and ternary eutectic transfers from regular to anomalous structure. When undercooling exceeds 102 K, anomalous (ε+θ+Sb) ternary eutectic is the unique microstructure. Competitive nucleation and growth of these three eutectic phases is the main cause for the formation of complex growth morphologies. Based on the current experiments and theoretical calculations, it can be concluded that the intermetallic compound phase θ(Cu2Sb) is the leading nucleating phase.