  We perform a model study of deconfinement and chiral symmetry restoration in
a strong magnetic background. We use a Nambu-Jona Lasinio model with the
Polyakov loop, taking into account a possible dependence of the coupling on the
Polyakov loop expectation value, as suggested by the recent literature. Our
main result is that, within this model, the deconfinement and chiral crossovers
of QCD in strong magnetic field are entangled even at the largest value of $eB$
considered here, namely $eB=30 m_\pi^2$ (that is, $B \approx 6\times 10^{15}$
Tesla). The amount of split that we measure is, at this value of $eB$, of the
order of 2%. We also study briefly the role of the 8-quark term on the
entanglement of the two crossovers. We then compare the phase diagram of this
model with previous results, as well as with available Lattice data.
