  A comprehensive study of $b\to c$ weak decays of doubly heavy baryons is
presented in this paper. The transition form factors as well as the pole
residues of the initial and final states are respectively obtained by
investigating the three-point and two-point correlation functions in QCD sum
rules. Contributions from up to dimension-6 operators are respectively
considered for the two-point and three-point correlation functions. The
obtained form factors are then applied to a phenomenological analysis of
semi-leptonic decays.
