Magnetoconductivity of ten ZnO, Zn1_xCoxO, and Zn1_xMnxO thin films with nominal concentrations of 2.0 at.% and 0.1 at.% of Co2þ and Mn2þ ions, respectively, has been analyzed in the temperature range from 5 K to 200 K in in-plane and out-of-plane magnetic fields up to 6 T. The formation of a highly conducting surface layer can be controlled during thin film deposition, leading to a large variation of the sheet resistance, namely, from 2 _ 103 Ω/A to 1 _ 105 Ω/A at room temperature. Depending on the thickness of the highly conducting surface layer, a single two-dimensional (2D), a single three-dimensional (3D), or a two-dimensional and three-dimensional (2D + 3D) parallel conducting model was chosen to analyze the measured magnetoconductivity of the magnetic ZnO thin films with different electron spins (S ¼ 5=2 for Zn1_xMnxO and S ¼ 3=2 for Zn1_xCoxO) and with different Landé g-factors (isotropic for 3D Zn1_xMnxO and 2D Zn1_xCoxO and anisotropic for 2D Zn1_xMnxO and 3D Zn1_xCoxO).