This work deals with structural and dynamical properties of copolymer gels containing free branched chains which were prepared by styrene-butadiene emulsion copolymerization. The gel fraction of the emulsion copolymers was varied within a large range (15-90 %) by adding different chain transfer agents during the polymerization process. NMR experiments were performed on homogeneous polymer films obtained by coalescence of the particles upon drying of the dispersions. Properties of dry extracted gels, gels swollen by free chains, or gels fully swollen by a good solvent were investigated to bring out the statistical structure of the gels. A time-temperature superposition principle was found to provide a good analysis of the time dependence of the transverse magnetic relaxation functions. The temperature dependence of the scale factors reveals the strong role played by the free chains in the system. Finally, through the description of the state of constraints encountered by chain segments, NMR and viscoelastic features of these partly cross-linked systems are shown to be consistently interrelated.