  Beta Laguerre ensembles which are generalizations of Wishart ensembles and
Laguerre ensembles can be realized as eigenvalues of certain random tridiagonal
matrices. Analogous to the Wishart ($\beta=1$) case and the Laguerre ($\beta =
2$) case, for fixed $\beta$, it is known that the empirical distribution of the
eigenvalues of these ensembles converges weakly to Marchenko--Pastur
distributions, almost surely. The paper restudies the limiting behavior of the
empirical distribution but in regimes where the parameter $\beta$ is allowed to
vary as a function of the matrix size $N$. We show that the above
Marchenko--Pastur law holds as long as $\beta N \to \infty$. When $\beta N \to
2c \in (0, \infty)$, the limit is related to associated Laguerre orthogonal
polynomials. Gaussian fluctuations around the limit are also studied.
