  A family of random matrix ensembles interpolating between the GUE and the
Ginibre ensemble of $n\times n$ matrices with iid centered complex Gaussian
entries is considered. The asymptotic spectral distribution in these models is
uniform in an ellipse in the complex plane, which collapses to an interval of
the real line as the degree of non-Hermiticity diminishes. Scaling limit
theorems are proven for the eigenvalue point process at the rightmost edge of
the spectrum, and it is shown that a non-trivial transition occurs between
Poisson and Airy point process statistics when the ratio of the axes of the
supporting ellipse is of order $n^{-1/3}$. In this regime, the family of
limiting probability distributions of the maximum of the real parts of the
eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.
