  Let $(G\rr P, \mathsf D_G)$ be a Dirac groupoid. We show that there are
natural Lie algebroid structures on the units $\lie A(\mathsf D_G)$ and on the
core $I^\tg(\mathsf D_G)$ of the multiplicative Dirac structure. In the Poisson
case, the Lie algebroid $A^*G$ is isomorphic to $\lie A(\mathsf D_G)$ and in
the case of a closed 2-form, the $IM$-2-form is equivalent to the core
algebroid that we find. We construct a vector bundle $\lie B(\mathsf D_G)\to P$
associated to any (almost) Dirac structure. In the Dirac case, $\lie B(\mathsf
D_G)$ has the structure of a Courant algebroid that generalizes the Courant
algebroid defined by the Lie bialgebroid of a Poisson groupoid. This Courant
algebroid structure is induced in a natural way by the ambient Courant
algebroid $TG\oplus T^*G$. The already known theorems about one-one
correspondence between the homogeneous spaces of a Poisson Lie group
(respectively Poisson groupoid, Dirac Lie group) and suitable Lagrangian
subspaces of the Lie bialgebra or Lie bialgebroid are generalized to a
classification of the Dirac homogeneous spaces of a Dirac groupoid. $\mathsf
D_G$-homogeneous Dirac structures on $G/H$ are related to suitable Dirac
structures in $\lie B(\mathsf D_G)$. In the case of almost Dirac structures, we
find Lagrangian subspaces of $\lie B(D_G)$, that are invariant under an induced
action of the bisections of $H$ on $\lie B(\mathsf D_G)$.
