We address the fundamental question of whether magnetoresistance (MR) of atomic-sized contacts of nickel is very large because of the formation of a domain wall (DW) at the neck. Using ab initio transport calculations we find that, as in the case of nonmagnetic electrodes, transport in Ni nanocontacts depends very much on the orbital nature of the electrons. Our results are in agreement with several experiments in the average value of the conductance. On the other hand, contrary to existing claims, DW scattering does not account for large MR in Ni nanocontacts. ; J.J.P. acknowledges financial support from Grants No. 1FD97-1358 (FEDER funds) and MAT2002-04429-C03 (MCyT). D.J. acknowledges financial support from MECD under Grant No. UAC-2004-0052. J.F.R. acknowledges financial support from Grants No. MAT2003-08109-C02-01 (MCyT), UA/GRE03-15 (Universidad de Alicante), and Ramon y Cajal Program (MCyT).