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Using a high-resolution primitive equation model of the western Mediterranean Sea, we analyzed the dispersion properties of a set of homogeneously distributed, passive particle pairs. These particles were initially separated by different distances <i>D</i>₀ (<i>D</i>₀ = 5.55, 11.1 and 16.65 km), and were seeded in the model at initial depths of 44 and 500 m. <br><br> This realistic ocean model, which reproduces the main features of the regional circulation, puts into evidence the three well-known regimes of relative dispersion. <br><br> The first regime due to the chaotic advection at small scales lasts only a few days (3 days at 44 m depth, a duration comparable with the integral timescale), and the relative dispersion is then exponential. In the second regime, extending from 3 to 20 days, the relative dispersion has a power law <i>t</i>^&alpha; where α tends to 3 as <i>D</i>₀ becomes small. In the third regime, a linear growth of the relative dispersion is observed starting from the twentieth day. For the relative diffusivity, the <i>D</i>² growth is followed by the Richardson regime <i>D</i>^4/3. At large scales, where particle velocities are decorrelated, the relative diffusivity is constant. <br><br> At 500 m depth, the integral timescale increases (> 4 days) and the intermediate regime becomes narrower than that at 44 m depth due to the weaker effect of vortices (this effect decreases with depth). The turbulent properties become less intermittent and more homogeneous and the Richardson law takes place.