the occurrence of a finite correlation length in the boundary theory.\
The paper is organized as follows. In the section \[section strip BH f(z)\] we review the holographic prescription for the entanglement entropy, specializing the analysis to ansatz that contain the black hole metrics we consider in the rest of the paper. In the section \[section near horizon\] we study the finite term of the holographic entanglement entropy for the charged black hole, the warped black hole of [@Herzog:2009gd] and the perturbed Lifshitz background considered in [@Gubser:2009cg] as a solution of the Abelian Higgs model [@Gubser:2008px]. In the section \[section lifshitz bh\] we study the Lifshitz black hole of [@Balasubramanian:2009rx] computing the analytic expression of the holographic entanglement entropy to all orders in the UV cutoff. This allows us to extract the finite term and to test the method employed for the other black holes. In the section \[section 2 strips\] we consider two equal and parallel strips in the boundary and study the transition of the mutual information for $AdS_{d+2}$ and for the charged black hole.

Holographic entanglement entropy for black holes {#section strip BH f(z)}
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In this section we review the holographic prescription to compute the entanglement 