  We present quantum Monte Carlo (QMC) simulations for a single hole in a t-J
model from J=0.4t to J=4t on square lattices with up to 24 x 24 sites. The
lower edge of the spectrum is directly extracted from the imaginary time
Green's function. In agreement with earlier calculations, we find flat bands
around $(0,\pm\pi)$, $(\pm\pi,0)$ and the minimum of the dispersion at
$(\pm\pi/2,\pm\pi/2)$. For small J both self-consistent Born approximation and
series expansions give a bandwidth for the lower edge of the spectrum in
agreement with the simulations, whereas for J/t > 1, only series expansions
agree quantitatively with our QMC results. This band corresponds to a coherent
quasiparticle. This is shown by a finite size scaling of the quasiparticle
weight $Z(\vec k)$ that leads to a finite result in the thermodynamic limit for
the considered values of $J/t$. The spectral function $A(\vec k, \omega)$ is
obtained from the imaginary time Green's function via the maximum entropy
method. Resonances above the lowest edge of the spectrum are identified, whose
J-dependence is quantitatively described by string excitations up to J/t=2.
