  We study the condensation transition of counterions on a charged cylinder via
Monte Carlo simulations. Varying the cylinder radius systematically in relation
to the system size, we find that all counterions are bound to the cylinder and
the heat capacity shows a drop at a finite Manning parameter. A finite-size
scaling analysis is carried out to confirm the criticality of the complete
condensation transition, yielding the same critical exponents with the Manning
transition. We show that the existence of the complete condensation is
essential to explain how the condensation nature alters from continuous to
discontinuous transition.
