<p>In this paper we investigate a predator-prey reaction-diffusion system incorporating prey-taxis and nonlinear boundary conditions. The model describes the directed movement of predators toward higher prey densities, while nonlinear boundary conditions model the net flux of populations across the habitat boundary as a nonlinear function of their density. Using principal eigenvalue analysis and bifurcation theory, we derive criteria for the existence and stability of semi-trivial steady states. Furthermore, we prove the existence of local and global bifurcation of positive steady-state solutions from the prey-only equilibrium. Our results reveal that predator persistence is jointly determined by growth rates, predation efficiency, diffusion rates, and boundary-driven mortality. In particular, we identify critical thresholds for boundary loss rates, predator growth rates, and predation rates that govern the transition between extinction and coexistence, highlighting the ecological significance of dispersal strategies and habitat boundaries in shaping predator-prey dynamics.</p>