The transport properties of planar Fe/MgO/Fe tunnel junctions are investigated theoretically by means of ab initio calculations. In particular, the k
||-resolved conductance in dependence on the barrier thickness, the interface structure, and the magnetic configuration is studied. The results show that the number of states in the k
||-space contributing significantly to the overall current is decreasing with increasing barrier thickness as expected. In contrast to simple parabolic band models the contribution of states in the vicinity of k
||=0, however, is only involved for a few considered configurations of the system Fe/MgO/Fe.