simulation of association and dissociation of ions in an ionic fluid. The

method is then utilized to carry out extensive MC simulations, in order

to study the properties of ionic fluids in two-dimensional systems that

consist of mobile ions with and without the presence of a quenched disorder.

The size distributions of the ionic clusters, their

conformations, as well as the clusters' multipole distributions are computed

over wide ranges of temperature $T$ and ions' density $\rho$ as well as the

quench disorder density $\rho_q$ and quenching temperature $T_q$.

At any given $T$, bonded dipolar pairs are dominant in the insulating phase, but larger clusters

with an even number of ions are also present. In the conducting phase at the

same $T$, however, single (free) ions are abundant, while clusters of larger

sizes are also present. As for the conformations of the clusters, at any $T$

perturbed folded structures are dominant in the insulating phase, whereas

perturbed linear chains are the dominant conformation in the conducting phase

at the same $T$. Moreover, ionic clusters with closed loops are rarely formed,

if at all, over the range of $T$ that we study. As $T$ decreases, more clusters

with symmetrical conformations are formed. The multipole distributions are

shown to be accurate indicators for the various types of conformations of the

ionic clusters. They are also shown to be accurate means of differentiating the

conformations of ionic clusters that may appear to be only slightly different,

and may be difficult to distinguish otherwise, as the multipoles are sensitive

to the details of the conformations. Some exact results are presented for the

dipoles and quadrupoles of several types of cluster conformations. These

results give rise, for the first time, to a numerical ``spectroscopy'' of ionic

fluids, whereby each conformation is associated with distinct values of the

dipole and quadrupole of the ionic cluster. We also suggest a new method of

locating the critical locus $T_c(\rho)$ that separates the conducting and

insulating phases - the Kosterlitz-Thouless transition - based only on the the

size distribution of the ionic clusters and its dependence on the ions'

density.

We also found that the presence of the quench disorder and its strongly affect

the behavior of the system. An insulating quench, i.e. a disorder that is quenched

from an insulating fluid, weakly influences the behavior of mobile ions. On the other

hand a conducting quench, which is generated by quenching a conducting fluid,

strongly changes the behavior of the system.