We compute the excess number of counterions associated with kinked and branched DNA, and the ionic stabilities of these structures as a function of chain length and both sodium and magnesium salt concentration, using numerical counterion condensation theory. The DNA structures are modeled as two or more finite lines of phosphate charges radiating from the kink or junction center. The number of excess counterions around the (40-90 degrees) kinked duplex is very small (at most four). The geometries of large three- and four-way DNA junctions (with > 50 base pairs per arm) in solutions containing low to moderate NaCl concentrations, by contrast, accumulate a substantial number of excess sodium ions (> 20) but no more than 15 magnesium counterions. The excess number of counterions surrounding the kinked linear chain and the branched DNA structures either remains invariant or increases with chain length, tending to reach a plateau value. Open configurations, such as the planar Y-shaped three-way junction (with three 120 degrees inter-arm angles) and the 90 degrees cross-shaped four-way junction, are ionically more stable than compact geometries, such as pyramidal three-way junctions and X-shaped four-way junctions, over the entire range of salt concentration considered (10(-5)-10(-1) M NaCl or MgCl2). The ionic stabilities of the compact forms increase with increasing salt concentration and become comparable to those of the extended geometries at high salt (especially when magnesium is the supporting salt).