Spontaneous branching of discharge channels is frequently observed, but not well understood. We recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields. We here present analytical results for such streamers in the Lozansky-Firsov limit where they can be modeled as moving equipotential ionization fronts. This model can be analyzed by conformal mapping techniques which allow the reduction of the dynamical problem to finite sets of nonlinear ordinary differential equations. Our solutions illustrate that branching is generic for the intricate head dynamics of streamers in the Lozansky-Firsov limit. When nonionized matter is suddenly exposed to strong fields, ionized regions can grow in the form of streamers. These are ionized and electrically screened channels with rapidly propagating tips. The tip region is a very active impact ionization region due to the self-generated local field enhancement. Streamers appear in early stages of atmospheric discharges such as sparks or sprite discharges [1,2]; they also play a prominent role in numerous technical processes. It is commonly observed that streamers branch spontaneously [3,4]. But how this branching is precisely determined by the underlying discharge physics is essentially not known. In recent work [5,6], we have suggested a branching mechanism from first principles. This work drew some attention [7,8], since the proposed mechanism yields quantitative predictions for specific parameters, and since it is qualitatively different from the older branching concept of the "dielectric breakdown model" [9][10][11]. This older concept actually can be traced back to concepts of rare long-ranged (and hence stochastic) photoionization events probably first suggested in 1939 by Raether [12]. Therefore, it came as a surprise that we predicted streamer branching in a fully deterministic model. Since our evidence for the phenomenon was mainly from numerical solutions together with a physical interpretation, the accuracy of our numerical scheme was challenged [13,14]. Furthermore, some authors have argued previously [15,16] that in a deterministic discharge model such as ours, an initially convex streamer head never could become locally concave, and that hence the consecutive branching of the discharge channel would be unphysical.Therefore in the present paper, we investigate the issue by analytical means. We show that the convex-to-concave evolution of the streamer head with successive branching is generic for streamers in the Lozansky-Firsov limit [5,6,17]. We define the Lozansky-Firsov limit as the stage of evolution where the streamer head is almost equipotential and surrounded by a thin electrostatic screening layer. While in the original paper [17], only simple steady state solutions with parabolic head shape are discussed, we will show here that a streamer in the Lozansky-Firsov limit actually can exhibit a very rich head dynamics that includes spontaneous branching. Furthermore, our analytical solutions disprove t...