To understand the molecular architectures of styrene-butadiene four-arm star (SBS) copolymers, a size exclusion chromatography combined with laser light scattering (SEC-LLS) has been used to determine their weight-average molecular weight (M-W) and radius of gyration (< S-2>)(1/2)), and a new method for the establishment of the Mark-Houwink equation from one sample has been developed. Based on the Flory viscosity theory, we successfully have reduced the < S-2>(1/2) values of numberless fractions estimated from many experimental points in the SEC chromatogram to intrinsic viscosities ([eta]). For the first time, the dependences of < S-2 > 1/2 and [eta] on M-W for the four-arm star SBS in tetrahydrofuran at 25 degrees C were found, respectively, to be (S-2 1/2 = 2,62 X 10(-2) M (nm) and [eta] = 3.68 X 10(-2) M-W(0.64) (mL/g) in the M-W range from 1.4 X 10(5) to 3.0 X 10(5). From data of [eta] and < S-2>(1/2) for linear and star SBS, we have obtained the information about the branching, namely, the ratios (g and g') of < S-2> and [eta] for star SBS to that of the linear SBS of the same molecular weight, which agree with theoretical predictions. (c) 2005 Wiley Periodicals, Inc.