This paper presents the electronic properties of ultrathin epitaxial graphite films grown on the (0001) surface of 6H-SiC. These films, composed of typically three graphene sheets, exhibit remarkable 2D electron gas (2DEG) behavior. The films were characterized using surface-science techniques and show a wide range of conductance values, from 1.5 kΩ to 225 kΩ at 4 K, with positive magnetoconductance. Low resistance samples show characteristics of weak-localization in two dimensions, allowing for the estimation of elastic and inelastic mean free paths. The Hall resistance is linear up to 4.5 T, indicating n-type carriers with a density of 10¹² cm⁻² per graphene sheet. The most highly-ordered sample exhibits Shubnikov-de Haas oscillations, suggesting a potential new quantum Hall system. The high-mobility films can be patterned via conventional lithographic techniques, and the film conductance can be modulated using a top-gate electrode. These properties suggest potential applications in nano-patterned epitaxial graphene (NPEG) devices. The exceptional electronic transport properties of low-dimensional graphitic structures have been demonstrated in carbon nanotubes and nanotube-based transistors. Ballistic transport has been observed up to room temperature, and quantum interference effects at cryogenic temperatures. Simple nanotube transistors and interconnected logic gates have been demonstrated, relying on the ability to control the nanotube conductance via an electrostatic gate. The electronic properties of carbon nanotubes are shared by other low-dimensional graphitic structures, such as planar nanoscopic graphene ribbons. These ribbons can have either metallic or semiconducting electronic structures, depending on the crystallographic direction of the ribbon axis. If suitable methods are developed to support and align graphene sheets, it would be possible to combine the advantages of nanotube-like electronic properties with high-resolution planar lithography to achieve large-scale integration of ballistic devices. An essential difference between nanotubes and planar graphene ribbons is the presence of dangling bonds at the edges, which can be passivated with donor or acceptor molecules to tune the electronic properties. The paper also presents results showing the two-dimensional nature of electrical transport in ultrathin graphite (multilayered graphene) grown epitaxially on SiC(0001). The 6H-SiC substrate provides an insulating surface at temperatures below 50 K for n-type doping. Magnetoconductance measurements and the physics of weak-localization were used to determine transport parameters of the graphite 2DEG. The character of the magnetotransport/localization spans a wide range of behaviors, depending on the amount of disorder in the film or substrate. Quantum oscillations in the magnetoconductance and Hall resistance were found for the most ordered sample, suggesting theThis paper presents the electronic properties of ultrathin epitaxial graphite films grown on the (0001) surface of 6H-SiC. These films, composed of typically three graphene sheets, exhibit remarkable 2D electron gas (2DEG) behavior. The films were characterized using surface-science techniques and show a wide range of conductance values, from 1.5 kΩ to 225 kΩ at 4 K, with positive magnetoconductance. Low resistance samples show characteristics of weak-localization in two dimensions, allowing for the estimation of elastic and inelastic mean free paths. The Hall resistance is linear up to 4.5 T, indicating n-type carriers with a density of 10¹² cm⁻² per graphene sheet. The most highly-ordered sample exhibits Shubnikov-de Haas oscillations, suggesting a potential new quantum Hall system. The high-mobility films can be patterned via conventional lithographic techniques, and the film conductance can be modulated using a top-gate electrode. These properties suggest potential applications in nano-patterned epitaxial graphene (NPEG) devices. The exceptional electronic transport properties of low-dimensional graphitic structures have been demonstrated in carbon nanotubes and nanotube-based transistors. Ballistic transport has been observed up to room temperature, and quantum interference effects at cryogenic temperatures. Simple nanotube transistors and interconnected logic gates have been demonstrated, relying on the ability to control the nanotube conductance via an electrostatic gate. The electronic properties of carbon nanotubes are shared by other low-dimensional graphitic structures, such as planar nanoscopic graphene ribbons. These ribbons can have either metallic or semiconducting electronic structures, depending on the crystallographic direction of the ribbon axis. If suitable methods are developed to support and align graphene sheets, it would be possible to combine the advantages of nanotube-like electronic properties with high-resolution planar lithography to achieve large-scale integration of ballistic devices. An essential difference between nanotubes and planar graphene ribbons is the presence of dangling bonds at the edges, which can be passivated with donor or acceptor molecules to tune the electronic properties. The paper also presents results showing the two-dimensional nature of electrical transport in ultrathin graphite (multilayered graphene) grown epitaxially on SiC(0001). The 6H-SiC substrate provides an insulating surface at temperatures below 50 K for n-type doping. Magnetoconductance measurements and the physics of weak-localization were used to determine transport parameters of the graphite 2DEG. The character of the magnetotransport/localization spans a wide range of behaviors, depending on the amount of disorder in the film or substrate. Quantum oscillations in the magnetoconductance and Hall resistance were found for the most ordered sample, suggesting the