Polynomial maps with nilpotent Jacobians in dimension three II

In the paper, we first classify all polynomial maps of the form $H=(u(x,y),v(x,y,z),h(x,y))$ in the case that $JH$ is nilpotent and $({\mathrm{deg}}_{y}u,{\mathrm{deg}}_{y}h)\le 3$, $H(0)=0$. Then we classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,u),h(x,y))$ in the case that $JH$ is nilpotent and $(\mathrm{deg}v(x,y,0),\mathrm{deg}h)\le 3$, $H(0)=0$. Finally, we classify polynomial maps of the form $H=(u(x,y,z),v(x,y,z),h(x,y))$ in certain conditions.