  (abridged)We present a comprehensive characterization of the general
properties (luminosity functions, mass, size, ages, etc) of optically selected
compact stellar objects (knots) in a representative sample of 32 low-z
(U)LIRGs. We use ACS images from the Hubble Space Telescope in F435W and F814W
bands. The galaxies in the sample represent different interaction phases and
cover a wide luminosity range (11.46 \leq log (L_IR (Lsun)) \leq 12.54). With a
median size of 32 pc, most of the nearly 3000 knots detected consists of
complexes of star clusters. Some of the knots (~15%) are so blue that their
colors indicate a young (i.e., < 30 Myr) and almost extinction-free population.
There is a clear correlation of the mass of these blue knots with their radius,
M \propto R^{1.91\pm0.14}, similar to that found in complexes of clusters in
M51 and in Giant Molecular Clouds. This suggests that the star formation within
the knots is proportional to the gas density at any given radius. The star
formation of all the knots is characterized by luminosity functions (LFs) of
the knots with slopes close to 2. Though, we see a marginally significant
indication that the LF evolves with the interaction process, becoming steeper
from early to advanced merger phases. Due to size-of-sample effects we are
probably sampling knots in ULIRGs intrinsically more luminous (x4) than in less
luminous systems. They also have sizes and are likely to have masses
characteristic of clumps in galaxies at z \gtrsim 1. Knots in post-mergers are
on average larger (x 1.3-2), more luminous (2 mag) in the I-band, and 0.5 mag
redder than those in systems in earlier phases. Two scenarios are briefly
discussed: (1) the likely presence of relatively high extinction in the most
advanced mergers; (2) the dissolution of the less massive clusters and/or their
coalescence into more massive, evolved superclusters.
