Accretion onto supermassive black holes (BHs) can launch relativistic outflows and jets that inject energy and momentum into their surroundings. Understanding how such feedback shapes large-scale accretion is key to bridging observations from galactic scales (e.g., the Bondi radius, $r_{\mathrm{B}}$) down to event horizon scales ($r_{\mathrm{g}}$), spanning five to six orders of magnitude. To address this challenge directly, we treat the spatial scale separation as a free parameter, varying it across two to four orders of magnitude. We perform a suite of the longest contiguous 3D general relativistic magnetohydrodynamic simulations to date ($t\le 4\times {10}^6{r}_{\mathrm{g}}/c$), modeling Bondi-like accretion of rotating, nonrelativistic gas with weak vertical magnetic fields onto a rapidly spinning BH, achieving inflow equilibrium out to $r\gtrsim {10}^3{r}_{\mathrm{g}}$. We find that, regardless of scale separation or ambient gas rotation, all simulations reach a magnetically arrested disk (MAD) state in which the BH becomes magnetically saturated. In this state, the mass inflow rate follows a universal radial scaling relative to the Bondi rate: ${\dot{M}}_{\mathrm{in}}(r)/{\dot{M}}_{\mathrm{B}}\sim (r/r_{\mathrm{B}}{)}^s$ with $s=0.66\pm 0.03$. The MAD state self-regulates through jets, outflows, and magnetic flux eruptions that can ultimately disrupt coherent angular momentum inflow, giving rise to a rocking accretion disk (RAD) state. This RAD state features chaotically oriented inflows, weak intermittent jets, and a steeper inflow slope of $s=0.87\pm 0.05$, along with significantly weaker outflows. For rapidly spinning BHs, the MAD and RAD BH accretion rates become comparable at typical scale separations, $r_{\mathrm{B}}/r_{\mathrm{g}}\gtrsim {10}^5$. The weaker outflows in the RAD state allow large-scale inflows to resume, eventually restoring the MAD state and enabling a repeating MAD-RAD cycle. We find that the MAD-RAD timescales can last from a few to hundreds of Bondi timescales, $t_{\mathrm{B}}\sim 0.2\mathrm{Myr}\times (r_{\mathrm{B}}/{10}^5{r}_{\mathrm{g}}{)}^{3/2}\times (M_{\mathrm{BH}}/{10}^9{M}_{\odot })$, where $M_{\mathrm{BH}}$ is the BH mass, potentially setting the duty cycle of jetted active galactic nucleus outbursts, like M87*.

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• Astrophysical fluid dynamics
• Accretion disk & black-hole plasma