Using a set of ROSAT HRI deep pointings, we investigate the presence o
f small-scale structures in the central regions of clusters of galaxie
s. Our sample comprises 23 objects up to z = 0.32, 13 of them known to
host a cooling flow. Structures are detected and characterized using
a wavelet analysis, their statistical significance being assessed by a
rigorous treatment of photon noise. For all clusters, we present mult
iresolution filtered images, restoring structures on all scales and al
lowing the suppression of noise. We then investigate in detail the geo
metrical properties of the smallest scale structures. Contrary to prev
ious claims, we find very few ''filaments'' or pointlike features at a
3.7 sigma level, except at the very cluster centers. Complex cores ar
e conspicuous in at least three massive cooling flows located at z = 0
.22 - 0.26. From our initial data set we have simulated a redshifted s
ample, and analyzed it in the same way in order to investigate any ins
trumental/resolution effect on the detectability of structures. On the
one hand, the topology of the core down to the limiting resolution ap
pears to be, at least in our redshift range, indistinguishable between
low and high z clusters. On the other hand, external parts seem to be
more affected in distant clusters, as indicated by the study of the '
'centroid shift'' or position angle variation as a function of radius.
Peculiar central features and strong isophotal twisting are found in
some distant massive cooling flow clusters. All this suggests that X-r
ay cores which extend to a region comparable to the cD envelope should
be rather isolated from the rest of the cluster and are probably unde
rgoing peculiar physical processes - like ISM/ICM connections - compet
ing with relaxation.