Planning realizable and stable grasps on 3D objects is crucial for many robotics applications, but grasp planners often ignore the relative sizes of the robotic hand and the object being grasped or do not account for physical joint and positioning limitations. We present a grasp planner that can consider the full range of parameters of a real hand and an arbitrary object, including physical and material properties as well as environmental obstacles and forces, and produce an output grasp that can be immediately executed. We do this by decomposing a 3D model into a superquadric 'decomposition tree' which we use to prune the intractably large space of possible grasps into a subspace that is likely to contain many good grasps. This subspace can be sampled and evaluated in GraspIt!, our 3D grasping simulator, to find a set of highly stable grasps, all of which are physically realizable. We show grasp results on various models using a Barrett hand.