We use molecular dynamics simulations to characterize spatiotemporal, high-mobility domains in various bulk polymers, thin slabs, and isolated chains as liquid samples are cooled across the glass transition. We define high-mobility domains as clusters, in space and time of torsional transition events along the polymers' backbones (dihedral angles switching between low-energy states). We confirm a linear relationship between the activation energy associated with such torsional transition events and the observed glass transition temperature across all systems studied. Furthermore, we find that the high-mobility domains percolate throughout the systems as the temperature is increased across the glass transition. Importantly, we observe identical percolation behavior in bulk systems, thin slabs, and small isolated chains (down to 100-monomer), even when the overall torsional relaxation rates increase significantly with free surface. Our results indicate that important dynamical features of undercooled polymers remain intact even in nanoscale systems.