We report magneto-crystalline anisotropy (MCA) calculations of Fe, Co and Ni slabs of various thicknesses and crystallographic orientations from two Density Functional Theory codes based either on a plane wave or a local atomic basis set expansion and a magnetic tight-binding method. We analyze the evolution of the MCA with the number of layers of the slabs. The decomposition of MCA into contributions of atomic sites helps understanding the oscillatory behaviour of the MCA with the slab thickness and highlights the role of finite size effects. We also identify some specific systems with enhanced MCA. A k-space as well as a band-filling analysis show very rich features of the MCA that could be used to tailor systems with enhanced magnetic properties. Finally this work can serve as a benchmark for MCA calculations.