  In this paper, the authors show the existence of global in time classical
solutions to the 3D quasi-geostrophic system with Ekman pumping for any smooth
initial value (possibly large). This system couples an inviscid transport
equation in $\mathbb{R}^3_+$ with an equation on the boundary satisfied by the
trace. The proof combines the De Giorgi regularization effect on the boundary
$z=0$ -similar to the so called surface quasi-geostrophic equation- with
Beale-Kato-Majda techniques to propagate regularity for $z>0$. A potential
theory argument is used to strengthen the regularization effect on the trace up
to the Besov space $\mathring{B}_{\infty,\infty}^1$.
