In the reactive off-axis sputtering deposition of ZnO films, three transport regimes from a ballistic motion to a diffusive drift of the ejected species were observed when the growth pressures were varied from 5 to 150 mTorr, The distribution of the film thickness at different substrate locations was measured, When the substrate surface was parallel to the gravity vector, a film thickness variation along the direction of gravity was detected in the region of diffusive transport deposition. This phenomenon depends strongly on the growth pressures while only slightly on the growth temperatures. Based on experimental results, a gravity-related motion of the sputtered species is proposed in film growth under relative low growth pressures.