Here we present a more detailed picture of some spatial properties of
the spin-polaron - quasiparticle formed after injecting a hole into a
planar quantum antiferromagnet. The explicit form of the quasiparticle
wave function allows us accurately to investigate the spatial extent
of the polaron. In the Ising limit of the model we find for the RMS ra
dius of the distribution of spin-deviations around the moving hole is
R = 1.06(t/J)(0.157). The form and the size of the polaron in the usua
l t-J model (Heisenberg limit), is on the other hand, anisotropic, lar
ger and does not obey such a simple scaling. Finally we discuss the re
normalization of spin-polarons by phonons in the framework of a Holste
in t-J model.