This work expands recent investigations in the field of spin-polarized tritium ͑T↓͒ clusters. We report the results for the ground-state energy and structural properties of large T↓ clusters consisting of up to 320 atoms. All calculations have been performed with variational and diffusion Monte Carlo methods, using an accurate ab initio interatomic potential. Our results for N Յ 40 are in good agreement with results obtained by other groups. Using a liquid-drop expression for the energy per particle, we estimate the liquid equilibrium density, which is in good agreement with our recently obtained results for bulk T↓. In addition, the calculations of the energy for large clusters have allowed for an estimation of the surface tension. From the mean-square radius of the drop, determined using unbiased estimators, we determine the dependence of the radii on the size of the cluster and extract the unit radius of the T↓ liquid.