  The space of one-dimensional disordered interacting quantum models displaying
a Many-Body-Localization Transition seems sufficiently rich to produce critical
points with level statistics interpolating continuously between the Poisson
statistics of the Localized phase and the Wigner-Dyson statistics of the
Delocalized Phase. In this paper, we consider the strong disorder limit of the
MBL transition, where the critical level statistics is close to the Poisson
statistics. We analyse a one-dimensional quantum spin model, in order to
determine the statistical properties of the rare extensive resonances that are
needed to destabilize the MBL phase. At criticality, we find that the
entanglement entropy can grow with an exponent $0<\alpha < 1$ anywhere between
the area law $\alpha=0$ and the volume law $\alpha=1$, as a function of the
resonances properties, while the entanglement spectrum follows the strong
multifractality statistics. In the MBL phase near criticality, we obtain the
simple value $\nu=1$ for the correlation length exponent. Independently of the
strong disorder limit, we explain why for the Many-Body-Localization transition
concerning individual eigenstates, the correlation length exponent $\nu$ is not
constrained by the usual Harris inequality $\nu \geq 2/d$, so that there is no
theoretical inconsistency with the best numerical measure $\nu = 0.8 (3)$
obtained by D. J. Luitz, N. Laflorencie and F. Alet, Phys. Rev. B 91, 081103
(2015).
