What is the ideal shape for a Van de Graaff generator dome? That is the question that lead to writing this utility. The resulting simulations show that indeed the best shape is one not so easy to fabricate.
Static charge on a conductor tends to maximize on sharp points and minimize on gentle curves. But this is not universally true, as can be seen here.
The final charge distribution predicted by this simulation is believed to be an accurate representation of the final charge distribution on a real conductor. On the other hand, the movement of charges as this simulation runs is definitely not like that of a real conductor. This is because the simulation model is different than a real conductor. In the simulation model, the conductor has no charges, other than the added charges to be distributed. In a real conductor, every atom has positive and negative charges. The simulation model differs from reality because of compute time limitations. In the simulation, a charge may move all the way from one end of the conductor to the other as equilibrium is being reached. In a real conductor, many free electrons would move a tiny bit to produce the same net charge movement.