International audienceLow Frequency Quasi-Periodic Oscillations or LF QPOs are ubiquitous in BH X-ray binaries and provide strong constraints on the accretion-ejection processes. Although several models have been proposed so far, none has been proven to reproduce all observational constraints and no consensus has emerged yet. We make the conjecture that disks are threaded by a large scale vertical magnetic field that splits it into two radial zones. In the inner Jet Emitting Disk (JED), a near equipartition field allows to drive powerful self-collimated jets, while beyond a transition radius, the disk magnetization is too low and a Standard Accretion Disk (SAD) is settled. In a series of papers, this hybrid JED-SAD disk configuration has be...