  We test whether static charged dilaton black holes in 2+1 dimensions can be
turned into naked singularities, by sending in test particles from infinity. We
derive that overcharging is possible and generic for both extremal and nearly
extremal black holes. Our analysis also imply that nearly extremal charged
dilaton black holes can be continuously driven to extremality and beyond,
unlike nearly extremal Ba\u{n}ados-Teitelboim-Zanelli, Kerr and
Reissner-Nordstr\"{o}m black holes which are overspun or overcharged by a
discrete jump. Thus the weak form of the cosmic censorship conjecture and the
third law of black hole thermodynamics are both violated in the interaction of
charged dilaton black holes in 2+1 dimensions, with test particles. We also
derive that there exists no points where the heat capacity vanishes or diverges
in the transition from black holes to naked singularities. The phase
transitions that could potentially prevent the formation of naked singularities
do not occur.
