A nearly isothermal heat pipe heat sink is provided. The heat sink includes a flat heat pipe connected to one or more flat vapor chambers using a conduit and a heat pipe. The connected flat heat pipe and the flat vapor chambers form a common vapor domain. Fins are attached on the outer surfaces of the flat heat pipe and the flat vapor chambers. Various capillary structures are also provided for fabricating flat heat pipes. A panelized welding process is further provided for fabricating flat heat pipes or flat vapor chambers. The panelized welding process uses either friction stir welding (FSW) or plasma beam welding to transversely join the panels that form the flat heat pipes or the flat vapor chambers.