We report aqueous self-assembly of linear amphiphilic triblock copolymers,poly(ethylene oxide)-block-polycaprolactone-block-poly(2-methyl-2-oxazoline) (PEO-b-PCL-b-PMOXA) and their PEO-b-PCL precursors with different PCL and PMOXA block lengths using three preparation methods: film rehydration, solvent evaporation, and cosolvent. For PEO-b-PCL, the self-assembled structures were ordinary spherical particles and polymersomes. For PEO-b-PCL-b-PMOXA, we observed polymersomes with asymmetric membrane, cloud-like aggregates, elongated particles, Y-shaped elongated particles, and 3D networks. All structures were of micrometer size and characterized using laser scanning microscopy (LSM). 3D networks were also characterized using z-stack confocal LSM, transmission electron microscopy (TEM), and cryogenic TEM. We demonstrated that film rehydration method results in pseudoequilibrium structures, whereas film rehydration aqueous self -assembly solvent evaporation cosolvent structures formed using solvent evaporation and cosolvent methods are under kinetic control. We showed how kinetically controlled structures can be transformed into pseudoequilibrium morphologies.