  We investigate the phenomenon of counterion condensation in a solution of
highly charged rigid polyelectrolytes within the cell model. A method is
proposed which -- based on the charge distribution function -- identifies both
the fraction of condensed ions and the radial extension of the condensed layer.
Within salt-free Poisson-Boltzmann (PB) theory it reproduces the well known
fraction 1-1/xi of condensed ions for a Manning parameter xi>1. Furthermore, it
predicts a weak salt dependence of this fraction and a breakdown of the concept
of counterion condensation in the high salt limit. We complement our
theoretical investigations with molecular dynamics simulations of a cell-like
model, which constantly yield a stronger condensation than predicted by PB
theory. While the agreement between theory and simulation is excellent in the
monovalent, weakly charged case, it deteriorates with increasing electrostatic
interaction strength and, in particular, increasing valence. For instance, at a
high concentration of divalent salt and large xi our computer simulations
predict charge oscillations, which mean-field theory is unable to reproduce.
