The streamer propagation in point-plane, non-uniform gaps under high applied electric fields, prior to the impact of primary streamer on cathode, is analyzed. The configuration used is an anode hyperboloid with 50-μm radius of curvature, and a flat plate as the cathode. The applied voltage is 130-kV direct current, and an initial electron is assumed to exist close to the anode in ambient air. The geometry used is a two-dimensional axisymmetry with a gap of 5 cm between the anode and the cathode. It is shown that the streamer is formed on the anode tip as expected, and midway toward the cathode, it separates into two streamers, the primary streamer that continues its propagation toward the cathode, and the branched streamer expanding radially toward the outer boundaries. The qualitative behavior of the discharge is analyzed in terms of streamer speeds, radial and axial electric fields, charged particle densities, and conductive currents. A branched streamer plasma structure was observed along the path of the primary plasma structure expanding radially outwards.