Controllable 3D human avatars have found widespread applications in 3D games, the metaverse, and AR/VR scenarios. The conventional approach to creating such a 3D avatar requires a lengthy, intricate pipeline encompassing appearance modeling, motion planning, rigging, and physical simulation. In this paper, we introduce UNICA (UNIfied neural Controllable Avatar), a skeleton-free generative model that unifies all avatar control components into a single neural framework. Given keyboard inputs akin to video game controls, UNICA generates the next frame of a 3D avatar's geometry through an action-conditioned diffusion model operating on 2D position maps. A point transformer then maps the resulting geometry to 3D Gaussian Splatting for high-fidelity free-view rendering. Our approach naturally captures hair and loose clothing dynamics without manually designed physical simulation, and supports extra-long autoregressive generation. To the best of our knowledge, UNICA is the first model to unify the workflow of "motion planning, rigging, physical simulation, and rendering". Code is released at https://github.com/zjh21/UNICA.