  We have recently performed a relativistic $O(q^4)$ chiral expansion of the
two-pion exchange $NN$ potential, and here we explore its configuration space
content. Interactions are determined by three families of diagrams, two of
which involve just $g_A$ and $f_{\pi}$, whereas the third one depends on
empirical coefficients fixed by subthreshold $\pi N$ data. In this sense, the
calculation has no adjusted parameters and gives rise to predictions, which are
tested against phenomenological potentials. The dynamical structure of the
eight leading non-relativistic components of the interaction is investigated
and, in most cases, found to be clearly dominated by a well defined class of
diagrams. In particular, the central isovector and spin-orbit, spin-spin, and
tensor isoscalar terms are almost completely fixed by just $g_A$ and $f_{\pi}$.
The convergence of the chiral series in powers of the ratio (pion mass/nucleon
mass) is studied as a function of the internucleon distance and, for $r>$ 1 fm,
found to be adequate for most components of the potential. An important
exception is the dominant central isoscalar term, where the convergence is
evident only for $r>$ 2.5 fm. Finally, we compare the spatial behavior of the
functions that enter the relativistic and heavy baryon formulations of the
interaction and find that, in the region of physical interest, they differ by
about 5%.
