The routines are
magma_*getrf() for LU,
magma_*potrf() for Cholesky,
magma_*qrtrf() for QR.
These automatically do out-of-core computation, so the regular testing_*trf sample code should work, given a large matrix.
An out-of-core triangular solve is not currently available in MAGMA, so you have to use LAPACK's triangular solve, getrs() or potrs(). Similarly for QR, use LAPACK's unmqr or ungqr.