Nonlinear amphiphilic block copolymer architectures with precisely controlled structures bring new challenges to biomedical materials research. The paper describes the straightforward synthesis of new “snake tongue“ Y-shaped terpolymers containing poly(ethylene oxide) (PEO), poly(2-ethyl-2-oxazoline) (PEtOx) and poly(ε-caprolactone) (PCL) blocks into structure [AB(C)₂] (herein referred to as [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×44], [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×87], [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×131]). A series of well-defined Y-shaped terpolymers were successfully synthesised by a combination of living cationic and anionic ring-opening polymerization (ROP). The selected Y-shaped [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×44] terpolymer self-assembly was characterised in detail by static and dynamic light scattering, nanoparticle tracking analysis and cryo-transmission electron microscopy. The physico-chemical properties as well as the molecular architecture effect on the self-assembled structures and on the LCST were compared with the Y-shaped [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×87] and the [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×131] terpolymers. The results indicated a temperature-induced aggregation with an LCST between 60–63 °C for the [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×44], at 60 °C for the [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×87] and between 45–50 °C for the [MPEO₄₄-b-PEtOx₂₅₂-b-(PCL)_2×131] with significant differences in the supramolecular self-assembly behaviour compared with the analogous linear structure, clearly indicating the crucial effect of the molecular architecture. Furthermore, the increase of the molecular weight fraction of the hydrophobic block on the Y-shaped triblock terpolymers likely induced a decrease of the LCST.