We review some of our recent experimental studies on low-carrier concentration, mesoscopic two-dimensional electron gases (m2DEGs). The m2DEGs show a range of striking characteristics including a complete avoidance of the strongly localised regime even when the electrical resistivity $\rho >>h/e2$, giant thermoelectric response, and an apparent decoupling of charge and thermoelectric transport. We analyse the results and demonstrate that these observations can be explained based on the assumption that the charge carriers retain phase coherence over the m2DEG dimensions. Intriguingly, this would imply phase coherence on lengthscales of up to 10 $\mu$m and temperature $T$ up to 10 K which is significantly greater than conventionally expected in GaAs-based 2DEGs. Such unprecedentedly large phase coherence lengths open up several possibilities in quantum information and computation schemes.