  The quantum Hall effect in a 2D electron system expresses a topological
invariant, leading to a quantized conductivity. The thermal Hall and
thermoelectric Nernst conductances in two dimensions are also reported to be
quantized in specific systems. However, a comprehensive study of these
quantities within one formalism for quantum Hall systems is so far elusive. In
this work, we investigate the Hall, thermal Hall, and Nernst effects
analytically and numerically in 2D and 3D. In addition to the quantized values
for the Hall and thermal Hall conductances in two dimensions, we also find
quasi-quantized values in three dimensions, which are the related 2D quanta
scaled by a characteristic length. The Nernst conductivity is not generally
quantized. Instead, an integration in energy is required to obtain a
universally (quasi-)quantized thermoelectric quantity.
