<p>Controlling the flow of angular momentum in solids is central to next-generation electronic technologies, particularly in spintronics and the emerging field of orbitronics, where the orbital motion of electrons plays an active role. However, predicting how these quantities behave in realistic materials with surfaces, interfaces, and disorder remains a major theoretical challenge. To address this problem, we develop a real-space first-principles method based on density functional theory to investigate orbitronic phenomena in transition metals. Using the Real-Space Linear Muffin-Tin Orbital method within the Atomic Sphere Approximation (RS-LMTO-ASA) combined with a Chebyshev polynomial expansion of the Green’s functions, we compute orbital (spin) Hall transport and orbital (spin) accumulation directly in real space. The approach scales linearly with the number of nonequivalent atoms in the unit cell and naturally incorporates disorder, finite-size effects, and interface roughness. We apply the method to a wide range of transition-metal systems, computing bulk orbital and spin Hall conductivities, layer-resolved accumulations in finite slabs, and the corresponding responses in FM/TM bilayers. Our results capture both nonmagnetic and magnetic cases, demonstrating how surface and interfacial electronic structure, as well as broken time-reversal symmetry, modify the relation between bulk conductivities and local accumulations. Our methodology provides a scalable and flexible approach for realistic simulations of orbital transport phenomena in complex heterostructures.</p>