On the basis of the ellipsoidal vortex model and a Monte-Carlo-type diffusion simulation, we examine the flux and ensuing distribution of passive fluid particles through the boundary of an idealized geophysical vortex. Our focus is on features that the horizontal and vertical diffusion components introduce into the fluid particle transport. We examine the concurrent effect of both components, and we compare it with the only horizontal diffusion impact. We analyze the ellipsoid vortex model in two cases: (i) the steady state when the ellipsoid is motionless, i.e., there is no variation in its axes' lengths, and consequently the exterior fluid is not being stirred; (ii) the perturbed case when the ellipsoid rotates periodically, varying it axes' lengths, which results in the appearance of stirred fluid outside the ellipsoid. Influenced by diffusion, a fluid particle is now permitted to move to another vertical horizon, thus there is an increased possibility that the particle will eventually be located in the exterior stirred region rather than in the ellipsoid vortex with the regular dynamics. This is because the area of the horizontal section of the ellipsoid vortex decreases with depth, but the region of stirred exterior fluid extends significantly deeper. Numerical calculations show that factoring in the vertical component of diffusion significantly affects scalar spreading in the horizontal plane in the perturbed case, while in the steady state the vertical component of diffusion only induces dispersion linear growth according to a Gaussian distribution.