One illustrative method of forming a vertical transistor device disclosed herein includes, among other things, forming bottom source/drain (S/D) regions. A plurality of vertically oriented channel semiconductor structures is formed above the bottom source/drain (S/D) regions. A gate insulation layer is formed above the vertically oriented channel semiconductor structures. A conformal layer of conductive gate material is formed above the gate insulation layer. The conformal layer of conductive material is etched to define conductive gate spacers on sidewalls of the vertically oriented channel semiconductor structures. Top source/drain (S/D) regions are formed above the vertically oriented channel semiconductor structures.