Fast-moving accretors are a ubiquitous phenomenon in astrophysics. Their interaction with the surrounding gas can leave characteristic imprints on the form of morphological structures like bow shocks, Mach cones, and trails with different densities. We study how various physical processes affect the flow structure around an accretor with a one-way surface, its accretion rate, and accretion anisotropy. These processes correspond to distinct length scales: the Bondi radius, the stand-off distance of the bow shock, and the Hoyle-Lyttleton radius. We conducted adiabatic hydrodynamic simulations using a spherical coordinate grid centred on the accretor's location. By varying the accretor's (numerical) size across various scales — from much smaller than the stand-off distance to much larger than the Bondi radius — we analyse how the processes on these spatial scales affect the physics of the steady-state flow. All simulations achieve a steady state. When the accretor is smaller than the stand-off distance, a bow shock forms ahead of the object, and a nearly spherically symmetric atmosphere develops within this distance. Accretors smaller than the Hoyle-Lyttleton radius produce a Mach cone, while larger accretors exhibit a supersonic-to-subsonic flow transition on larger scales. Fully resolved simulations align with the Hoyle-Lyttleton theory, showing slightly anisotropic accretion with enhanced inflow from behind the object. In contrast, larger accretors approach the geometrical limit, with accretion primarily from the flow direction and a low-density `shadow' forming behind the object. The accretor's size greatly influences the small-scale and large-scale morphologies. Resolving the Hoyle-Lyttleton radius is essential for representing large-scale flow characteristics. Resolving the smaller stand-off distance is required only for studying the bow shock in front of the moving object: since the stand-off distance determines the bow shock's position, its non-resolution does not affect the larger-scale flow morphology.
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