We show that the complex of free factors of a free group of rank (Formula presented.) is homotopy equivalent to a wedge of spheres of dimension (Formula presented.). We also prove that for (Formula presented.), the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (Formula presented.) -connected. In addition, we show that for every non-trivial free factor system of a free group, the corresponding relative free splitting complex is contractible.