  Self-localization of holes in the Holstein t-J model is studied in the
adiabatic limit using exact diagonalization and the retraceable path
approximation. It is shown that the critical electron-phonon coupling \lambda_c
decreases with increasing J and that this behavior is determined mainly by the
incoherent rather than by the coherent motion of the hole. The obtained spin
correlation functions in the localized region can be understood within a
percolation picture where antiferromagnetic order can persist up to a
substantial hole doping. These results restrict the possibility of
self-localization of holes in lightly doped cuprates.
