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Observations of $\rm SgrA^*$ have provided a lot of insight on low-luminosityaccretion, with a handful of bright flares accompanied with orbital motionclose to the horizon. It has been proposed that gas supply comes from stellarwinds in the neighborhood of the supermassive black hole. We here argue thatthe flow at the vicinity of the black hole has a low magnetization and astructure of alternating polarity totally dictated by the well studied andlong-ago proposed MRI turbulent process. This can be the case, provided that inlarger distances from the black hole magnetic diffusivity is dominant and thusthe magnetic field will never reach equipartition values. For $\rm SgrA^*$, weshow the immediate consequences of this specific magnetic field geometry, whichare: (i) an intermittent flow that passes from quiescent states to flaringactivity, (ii) no quasi-steady-state jet, (iii) no possibility of amagnetically arrested configuration. Moreover a further distinctive feature ofthis geometry is the intense magnetic reconnection events, occurring as layersof opposite magnetic polarity are accreted, in the vicinity of the black hole.Finally, we argue that the absence of a jet structure in such case will be asmoking gun in 43 \& 86 GHz observations.

Magnetic field structure in the vicinity of a super-massive black hole in low luminosity galaxies: the case of Sgr A*