A series of seven fractions of branched polyethyleneimine (BPEI) spanning a molecular weight range 1.7 x 10(4)-5.3 x 10(6) gmol(-1) were characterized by means of laser light scattering and viscometry at 35 degrees C. The weight-average molecular weight, M(W), the second virial coefficient, A(2)*, the z-average radius of gyration, R(G), the z-average effective hydrodynamic radius, R(H), the intrinsic viscosity, [eta], and the Huggins coefficient, K-H, were determined in 1 M NaCl aqueous mixture solvent. Based upon these experimental results, the scaling relations between M, and the various kinds of radii were established. The exponents of the relations appeared to be much smaller than the generally accepted value for a linear polymer chain (for example, the Mark-Houwink equation; [eta] = 0.513 M(W)(0.31)). Also some ratios such as R(G)/R(H) and R(G)/R(T) showed a molecular weight dependence, where R(T) [= (3A(2)*M(W)(2)/16 pi N-A)(1/3)] was defined as the thermodynamic radius. Although quantitative comparison with theories was somewhat restricted due to the slightly high index of polydispersity (M(W)/M(n) = 1.8-2.2) of the BPEI fractions, it was found that the structure of BPEI seemed to be randomly branched and became more compact with increasing molecular weight.