Besides recovering the area law, this prescription passed many tests (e.g. the strong subadditivity inequalities) and it has been deeply studied (see the recent review [@Nishioka:2009un] and the references therein); thus it is considered a key tool to understand the essential features of the entanglement entropy for quantum field theories with a holographic dual.\
The entanglement entropy is not an extensive quantity, as can be easily understood e.g. by the fact that $S_A =S_B$ for a pure state (this equality is violated at finite temperature). In the holographic computation of the entanglement entropy extensivity is recovered if one considers the finite term of the minimal area (sometimes called renormalized entanglement entropy), i.e. the one obtained by subtracting the UV divergent term giving the area law, in a black hole background [@Ryu:2006ef; @Klebanov:2007ws; @Barbon:2008sr; @Barbon:2008ut]. This behavior is due to the fact that, as the size of the region $A$ in the boundary tends to infinity, a large part of the minimal surface gets very close to the horizon and this part goes like the volume of $A$ in the large size limit. Thus the near horizon geometry is responsible of the leading divergence of the finite term of the minimal 