  We provide a systematic quantitative description of spin polarization in
armchair and zigzag graphene nanoribbons in a perpendicular magnetic field. We
first address spinless electrons within the Hartree approximation studying the
evolution of the magnetoband structure and formation of the compressible
strips. We discuss the potential profile and the density distribution near the
edges and the difference and similarities between armchair and zigzag edges.
Accounting for the Zeeman interaction and describing the spin effects via the
Hubbard term we study the spin-resolved subband structure and relate the spin
polarization of the system at hand to the formation of the compressible strips
for the case of spinless electrons. At high magnetic field the calculated
effective g-factor varies around a value of <g*>~2.25 for armchair nanoribbons
and <g*>~3 for zigzag nanoribbons. An important finding is that in zigzag
nanoribbons the zero-energy mode remains pinned to the Fermi-energy and becomes
fully spin-polarized for all magnetic fields, which, in turn, leads to a strong
spin polarization of the electron density near the zigzag edge.
