Particles in nonthermal dusty plasmas tend to charge negatively. However several effects can result in a significant fraction of the particles being neutral or positively charged, in which case they can deposit on surfaces that bound the plasma. Monte Carlo charging simulations were conducted to explore the effects of several parameters on the non-negative particle fraction of the stationary particle charge distribution. These simulations accounted for two effects not considered by the orbital motion limited theory of particle charging: single-particle charge limits, which were implemented by calculating electron tunneling currents from particles; and the increase in ion current to particles caused by charge-exchange collisions that occur within a particle's capture radius. The effects of several parameters were considered, including particle size, in the range 1-10 nm; pressure, ranging from 0.1 to 10 Torr; electron temperature, from 1 to 5 eV; positive ion temperature, from 300 to 700 K; plasma electronegativity, characterized in terms of n (+)/n (e) ranging from 1 to 1000; and particle material, either SiO2 or Si. Within this parameter space, higher non-negative particle fractions are associated with smaller particle size, higher pressure, lower electron temperature, lower positive ion temperature, and higher electronegativity. Additionally, materials with lower electron affinities, such as SiO2, have higher non-negative particle fractions than materials with lower electron affinities, such as Si.