We present an atomistic simulation study on the size dependence of dopant distribution and the influence of nanoscale film thickness on carrier transport properties of the model oxide-ion conductor yttria stabilized zirconia (YSZ). Simulated amorphization and recrystallization approach was utilized to generate YSZ films with varying thicknesses (3-9 nm) on insulating MgO substrates. The atomic trajectories generated in the molecular dynamics simulations are used to study the structural evolution of the YSZ thin films and correlate the resulting microstructure with ionic transport properties at the nanoscale. The interfacial conductivity increases by 2 orders of magnitude as the YSZ film size decreases from 9 to 3 nm owing to a decrease in activation energy barrier from 0.54 to 0.35 eV in the 1200-2000 K temperature range. Analysis of dopant distribution indicates surface enrichment, the extent of which depends on the film thickness. The mechanisms of oxygen conductivity for the various film thicknesses at the nanoscale are discussed in detail and comparisons with experimental and other modeling studies are presented where possible. The study offers insights into mesoscopic ion conduction mechanisms in low-dimensional solid oxide electrolytes.