  We consider asymtotics of a domino tiling model on a class of domains which
we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the
corresponding height functions and provide explicit formulas for the limit. For
a special class of examples, the explicit parametrization of the frozen
boundary is given. It turns out to be an algebraic curve with very special
properties. Moreover, we establish the convergence of the fluctuations to the
Gaussian Free Field in appropriate coordinates. Our main tool is a recently
developed moment method for discrete particle systems.
