We present a comprehensive study of the conductance behavior of atomic-size contacts made of ferromagneti c metals (Co) or noble metals (Au) with ferromagneti c electrodes (Co). In order to separate the influence of the large electrodes fro m the influence of the contacts themse lves, we used different sampl e geometri es. T hese include combinati ons of nonmagnetic electrodes connected to magneti c bridges and vice versa as well as di fferent orientati ons of the mag netic fi eld. The magnetores istance (MR) curves show very rich behavi or with strong MR rati os (MRR). In all geometries the MRR va lu es are of comparabl e size, reaching up to a few thousand percent in the tunneli ng regime. We study the poss ibl e influence of the mi cromag neti c order of the domain s in the vic inity of the contac t as well as balli sti c MR, giant MR, tun nel MR , atomically enh anced ani sotropi c MR (AAMR), and magnetostri cti on. We co nclude that AAMR is the most important origin for the MR at hi gh magnet ic fie lds (iBI > 2 T) , while magnetostri ct ion, tunnel MR , and giant MR govern the low-fie ld reg ime (IBI < 2 T).