  We study the effect of spatial correlations in the quenched disorder on
random quantum magnets at and near a quantum critical point. In the random
transverse field Ising systems disorder correlations that decay algebraically
with an exponent rho change the universality class of the transition for small
enough rho and the off-critical Griffiths-McCoy singularities are enhanced. We
present exact results for 1d utilizing a mapping to fractional Brownian motion
and generalize the predictions for the critical exponents and the generalized
dynamical exponent in the Griffiths phase to d>=2.
