[en] Using a combination of Z-contrast imaging, scanning tunneling microscopy, and plan view diffraction contrast imaging, we have studied the growth and relaxation mechanisms of YBa₂Cu₃O_7-x deposited on MgO and SrTiO₃ substrates. Two-dimensional island growth occurs on SrTiO₃ substrates, with relaxation through the nucleation of dislocation half-loops. Then the threading dislocation segments with a screw component can lead to kinetic roughening through the development of growth pyramids. In contrast, growth on MgO occurs by true one-dimensional island growth (with no wetting layer), most of the interface being incommensurate with the substrate (although crystallographically aligned). Dislocations with both edge and screw components are generated on island coalescence. A highly anisotropic surface energy is shown to responsible for cell-by-cell c perpendicular growth being thermodynamically preferred, although at high supersaturations a transition a perpendicular growth occurs