  The recently discussed tendency of holes to generate nontrivial spin
environments in the extended two-dimensional t-J model (G. Martins, R. Eder,
and E. Dagotto, Phys. Rev. B{\bf 60}, R3716 (1999)) is here investigated using
computational techniques applied to ladders with several number of legs. This
tendency is studied also with the help of analytic spin-polaron approaches
directly in two dimensions. Our main result is that the presence of robust
antiferromagnetic correlations between spins located at both sides of a hole
either along the x or y axis, observed before numerically on square clusters,
is also found using ladders, as well as applying techniques based on a
string-basis expansion. This so-called "across-the-hole" nontrivial structure
exists even in the two-leg spin-gapped ladder system, and leads to an effective
reduction in dimensionality and spin-charge separation at short-distances, with
a concomitant drastic reduction in the quasiparticle (QP) weight Z. In general,
it appears that holes tend to induce one-dimensional-like spin arrangements to
improve their mobility. Using ladders it is also shown that the very small
J/t$\sim$0.1 regime of the standard t-J model may be more realistic than
anticipated in previous investigations, since such regime shares several
properties with those found in the extended model at realistic couplings.
Another goal of the present article is to provide additional information on the
recently discussed tendencies to stripe formation and spin incommensurability
reported for the extended t-J model.
