To elucidate the nature of load sharing in the growth of multiple biopolymers, we perform stochastic simulations of the growth of biopolymer bundles against obstacles under a broad range of conditions and varying assumptions. The obstacle motion due to thermal fluctuations is treated explicitly. We assume the "Perfect Brownian Ratchet" (PBR) model, in which the polymerization rate equals the free-filament rate as soon as the filament-obstacle distance exceeds the monomer size. Accurate closed-form formulas are obtained for the case of a rapidly moving obstacle. We find the following: (1) load sharing is usually sub-perfect in the sense that polymerization is slower than for a single filament carrying the same average force; (2) the sub-perfect behavior becomes significant at a total force proportional to the logarithm or the square root of the number of filaments, depending on the alignment of the filaments; (3) for the special case of slow barrier diffusion and low opposing force, an enhanced obstacle velocity for an increasing number of filaments is possible; (4) the obstacle velocity is very sensitive to the alignment of the filaments in the bundle, with a staggered alignment being an order of magnitude faster than an unstaggered one at forces of only 0.5 pN per filament for 20 filaments; (5) for large numbers of filaments, the power is maximized at a force well below 1 pN per filament; (6) for intermediate values of the obstacle diffusion coefficient, the shape of the force velocity relation is very similar to that for rapid obstacle diffusion.