  Very recently a conjecture saying that the so-called structural physical
approximations (SPAa) to optimal positive maps (optimal entanglement witnesses)
give entanglement breaking (EB) maps (separable states) has been posed [J. K.
Korbicz {\it et al.}, Phys. Rev. A {\bf 78}, 062105 (2008)]. The main purpose
of this contribution is to explore this subject. First, we extend the set of
entanglement witnesses (EWs) supporting the conjecture. Then, we ask if SPAs
constructed from other than the depolarizing channel maps also lead to EB maps
and show that in general this is not the case. On the other hand, we prove an
interesting fact that for any positive map $\Lambda$ there exists an EB channel
$\Phi$ such that the SPA of $\Lambda$ constructed with the aid of $\Phi$ is
again an EB channel. Finally, we ask similar questions in the case of
continuous variable systems. We provide a simple way of construction of SPA and
prove that in the case of the transposition map it gives EB channel.
