  We present a novel application of the recently developed AAA algorithm to the
solution of Laplace 2D problems; an application to conformal mapping is also
shown as a particular case. These classes of problems have also been addressed
by means of dedicated software implementations based on rational function
approximation, with unprecedented speed and accuracy. Still we show how the AAA
algorithm, conceived to be a flexible and domain independent method, is capable
of addressing these situations within a unified framework.
