  This article is devoted to the analysis of control properties for a heat
equation with singular potential $\mu/\delta^2$, defined on a bounded $C^2$
domain $\Omega\subset\mathbb{R}^N$, where $\delta$ is the distance to the
boundary function. More precisely, we show that for any $\mu\leq 1/4$ the
system is exactly null controllable using a distributed control located in any
open subset of $\Omega$, while for $\mu>1/4$ there is no way of preventing the
solutions of the equation from blowing-up. The result is obtained applying a
new Carleman estimate.
