  The known asymptotic relations interconnecting Jacobi, Laguerre, and Hermite
classical orthogonal polynomials are generalized to the corresponding
exceptional orthogonal polynomials of codimension $m$. It is proved that
$X_m$-Laguerre exceptional orthogonal polynomials of type I, II, or III can be
obtained as limits of $X_m$-Jacobi exceptional orthogonal polynomials of the
same type. Similarly, $X_m$-Hermite exceptional orthogonal polynomials of type
III can be derived from $X_m$-Jacobi or $X_m$-Laguerre ones. The quadratic
transformations expressing Hermite classical orthogonal polynomials in terms of
Laguerre ones is also extended to even $X_{2m}$-Hermite exceptional orthogonal
polynomials.
