The thickness a part needs to be is dependent on how big is it and how much stress it is under. The Z plaster used in the 3D printing process is like concrete, it is weak in shear with very little ductility. If you have a long moment arm or long cantilever it will likely cause a thin attachment point to break. In general small areas of a wall can be as thin as 0.04" but this is very fragile. Structural elements (those that we or you need to pick the model up by) need to be 0.08" to 0.1" on small models and 0.1" to 0.18" on larger models.