  Spin effects in the tunneling regime of strong field ionization of
hydrogenlike highly charged ions in linearly as well as circularly polarized
laser fields are investigated. The impact of the polarization of a laser field
on the spin effects are analyzed. Spin-resolved differential ionization rates
are calculated employing the relativistic Coulomb-corrected strong-field
approximation (SFA) developed in the previous paper of the series. Analytical
expressions for spin asymmetries and spin flip probability, depending on the
laser's polarization, are obtained for the photoelectron momentum corresponding
to the maximum of tunneling probability. A simpleman model is developed for the
description of spin dynamics in tunnel-ionization, which provides an intuitive
explanation for the spin effects. The spin flip is shown to be experimentally
observable by using moderate highly charged ions with a charge of the order of
20 and a laser field with an intensity of $I\sim 10^{22}$ W/cm$^2$.
