  Numerical simulations of the two-dimensional t-J model in the limit $J/t \ll
1$ are performed for rather large systems (up to $N = 12 \times 12$) using a
world-line loop-algorithm. It is shown that in the one-hole case with J=0,
where no minus signs appear, very low temperatures ($\beta t \sim 3000$) are
necessary in order to reach Nagaoka's state. $J/t \ltsim 0.05$ leads to the
formation of partially polarized systems, whereas $J/t \gtsim 0.05 $
corresponds to minimal spin. The two-hole case shows enhanced total spin up to
the lowest attainable temperatures ($\beta t = 150$).
