Recent experiments using Terawatt lasers to accelerate protons deposited on thin wire targets are modeled with a new type of gridless plasma simulation code. In contrast to conventional mesh-based methods, this technique offers a unique capability in emulating the complex geometry and open-ended boundary conditions characteristic of contemporary experimental conditions. Comparisons of ion acceleration are made between the tree code and standard particle-in-cell simulations for a typical collisionless “hole boring” scenario in slab geometry. The utility of the gridless approach is emphasized by a series of simulations in “wire” geometry, in which electrons are permitted to circulate around the target at arbitrary distances from the focal region. The simulations reveal a number of features in common with recent experimental observations, including a disclike emission pattern of the MeV protons accelerated away from the wire.