A scaling theory describing the equilibrium conformations of weakly charged, randomly branched polyelectrolytes in dilute and semidilute solutions is developed. We demonstrate that, in polydisperse dilute solution, small polymers are swollen by unscreened Coulomb repulsions between charged monomers while large polymers, in contrast, retain most of their counterions in the intramolecular space. As a result the intramolecular Coulomb repulsion in large polymers is partially screened. The effect of addition of salt is discussed and a power law dependence of the cluster size similar toN(1/2)c(s)(-1/5) is predicted. The concentration effects in a monodisperse salt-free solution of branched polyelectrolytes are considered. It is shown that, in the semidilute regime, the dimension of branched polyions scales as similar toN(1/3) and decreases with increasing polymer concentration because of additional screening of intramolecular Coulomb repulsion. Large clusters remain segregated (impermeable) in a wide range of the solution concentration while small clusters overlap partially.