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This study addresses the horizontal and vertical dispersion of passive tracers in idealized wind-driven subtropical gyres. Synthetic particles within a closed basin are numerically advected to analyze their dispersion under different theoretical velocity fields. Horizontal dispersion simulations incorporate the classic wind-driven Stommel circulation along with (i) surface Ekman drift associated with the Stommel wind field and (ii) inertial effects due to particle size and buoyancy. Results reveal that the Ekman drift inhibits particle dispersion across the entire domain leading to tracer concentration in a quasi-stable distribution skewed toward the western side of the basin. Similar behavior is observed with inertial particles. The equilibrium state is quantified for different diffusivity values, particle sizes, and buoyancies. For vertical dispersion, simulations incorporate the three-dimensional Ekman velocity, which includes a negative vertical component, while ignoring inertial effects. Initially, surface particles accumulate around the gyre center while slowly sinking, but they disperse across the basin once they surpass the Ekman layer and are free from surface effects. Tracers sink more on the western side of the basin, regardless of horizontal diffusivity. On average, ignoring inertial effects, particles sink less with higher diffusivity and more with lower diffusivity, suggesting a potential for high horizontal distribution of sunken tracers in the ocean.