  The objective of this paper is to help shedding some light on the nature and
the properties of the cold structures formed via thermal instability in the
magnetized atomic interstellar medium. To this end, we searched for clumps
formed in forced (magneto)hydrodynamic simulations with an initial magnetic
field ranging from 0 to 8.3$\mu$G. We statistically analyzed, through the use
of Kernel Density Estimations, the physical and the morphological properties of
a sample containing $\sim 1500$ clumps, as well as the relative alignments
between the main direction of clumps and the internal velocity and magnetic
field. The density ($n\sim 50-200$cm$^{-3}$), the thermal pressure
($P_{th}/k\sim 4.9\times 10^3-10^4$K cm$^{-3}$), the mean magnetic field ($\sim
3-11$$\mu$G ), and the sonic Mach number of the selected clumps have values
comparable to those reported in observations. We find, however, that the cloud
sample can not be described by a single regime concerning their pressure
balance and their Alf\'enic Mach number. We measured the morphological
properties of clumps mainly through the asphericity and the prolatness, which
appear to be more sensitive than the aspect ratios. From this analysis we find
that the presence of magnetic field, even if it is weak, does qualitatively
affect the morphology of the clumps by increasing the probability of having
highly aspherical and highly plolate clumps by a factor of two, that is by
producing more filamentary clumps. Finally, we find that the angle between the
main direction of the clumps and the local magnetic field lies between
$\sim\pi/4-\pi/2$ and shifts to more perpendicular alignments as the intensity
of this field increases, while the relative direction between the local density
structure and the local magnetic field transits from parallel to perpendicular.
