dependence of this result on the short range NN repulsion. On the other hand, the recent three body calculations based on Faddeev or AGS methods yield larger bindings. Thus Schevchenko *et al.* [@SHE07] obtain $( E_B, \Gamma) =
(55-70, 95-110) $ MeV while Ikeda and Sato [@IKE07] calculate $( E_B, \Gamma) = (\sim 80, \sim 73) $ MeV. Later in the text we show that the discrepancy of these two groups of results is due to: different $\Lambda(1405)$ properties, explicit description of the multiple scattering in decay channels and possibly to an incompatible treatment of the NN repulsion.

There are two new elements introduced in this paper. First, the P-wave interactions due to $\Sigma(1385)$ have been indicated as a possible source of the strong binding. Here, these are introduced explicitly. Second, the stress is put on the strong KN spacial correlations induced by the S and P wave resonances.

Leaving aside the interpretation of the peaks attributed to bound KNN and KNNN systems the essential theoretical questions are:

$(a)$ What is the binding mechanism?

$(b)$ Are the technical questions under control?

$(c)$ Can the widths be narrow?

This paper attempts an answer to these questions and the following results are 