  The out-of-plane g-factor g_perp for quasi-2D holes in a (100) GaAs
heterostructure is studied using a variable width quantum wire. A direct
measurement of the Zeeman splitting is performed in a magnetic field applied
perpendicular to the 2D plane. We measure an out-of-plane g-factor up to g_perp
= 5, which is larger than previous optical studies of g_perp, and is
approaching the long predicted but never experimentally verified out-of-plane
g-factor of 7.2 for heavy holes.
