Equilibrium conformations of star-branched polyelectrolytes in dilute solutions are studied on the basis of a numerical self-consistent-field (SCF) approach and analytical theories. It is shown that, even in a dilute salt-free solution, the intramolecular Coulombic repulsion in many-armed stars is strongly screened by counterions which are localized preferentially in the intrastar space. As a result, the dependence of the star size on the number of branches levels off for many-armed stars. Addition of salt results in additional screening and in contraction of the stars. The scaling prediction R similar to c(s)(-1/5) for the star size as a function of the salt concentration c(s) is well confirmed by SCF calculations. A decrease in the star size can also be induced by an increase in the concentration of the polyelectrolyte in the solution. We have observed significant contraction of the stars with increasing concentration below the overlap threshold, i.e. in dilute solutions. The latter effect is more pronounced for stars with a small number of branches. The screening of the intramolecular Coulombic repulsion due to added salt is compared with that occurring upon increasing the concentration of the polyelectrolyte.