The two-photon absorption properties of a set of linear copolymers based on the regular alternation of a 2,4,6-tris(thiophen-2-yl)-1,3,5-triazine electron-accepting unit with different electron-donating groups attached to two of the thiophen ends were investigated. Comparison of these data with those of the analogous octupolar monomers and hyperbranched polymers allows us to understand the role of the triazine-thiophen core and its molecular architecture in the nonlinear optical properties of these polymeric materials. It is concluded that the arrangement of the push-pull unit into a unidimensional array, as it is the case of the linear copolymer, favours the two-photon absorption cross-section. Hybrid nanoparticles dispersed in water were prepared from selected polymers with two-photon excited fluorescence emission comparable with those of the best performing quantum dots.