We have measured the conductivity sigma of TlX(X = Cl, Br, I) compounds up to 5.3 GPa and between 300-823 K. The sigma-T dependence for all compounds can be divided into three distinct regions : (i) low temperature (LT), < 400 K, with unusual negative sigma-T dependence, (ii) intermediate temperature (IT), 400 < 650 K, with positive sigma-T dependence and (iii) high temperature (HT), T > 650 K, with positive sigma-T dependence. The sigma-T isobars were used to construct the T-P solid phase diagram for each compound. The LT region data indicate a new meta-stable phase in the 1.0-3.5 GPa range. The LT --> IT transition is characterized by an inverse sigma-T dependence followed by normal Arrhenius behavior up to and including the HT region. The extrapolation to 1 atm of the P-dependent boundary between IT and I-IT regions above 3 GPa for each compound in the P-T plot yields a value close to its respective normal (1 atm) T-melt suggesting a solid order-disorder transition type paralleling alpha-AgI behavior. The abrupt drop in conductivity in the LT region for P between 2.5-4.1 GPa of all compounds is at variance with the Arrhenius behavior observed for unperturbed ion migration implying the appearance of a second factor overriding the Arrhenius temperature dependence. Normal Arrhenius sigma-T dependence prevails in both IT and HT regions with Q(c) values of 85-100 kJ mol(-1) and 50-75 kJ mol(-1), respectively. The higher conductivities at 0.4 GPa for TlBr and TlI relative to their 1 atm data and the increasing sigma with P are in strong contrast to the normal sigma-P behavior of TlCl. The dependence of activation volume Delta V double dagger on T for TlCl, i.e. Delta V double dagger > 0, shows abnormally high values with a maximum at 500 K for P < 3.0 GPa but reasonable Delta V double dagger values appear above 3.0 GPa. The Delta V double dagger-T dependence for both TlBr and TLI with Delta V double dagger < 0 is incompatible with an ion transport mechanism suggesting an electronic conduction process and implying an ionic-metallic transition at higher pressures. These contrasting conductivity features are discussed and interpreted in terms of electronegativity differences and bonding character rather than structure.