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Accretion discs in active galactic nuclei (AGNs) foster black hole (BH) formation, growth, and mergers. Stellar mass BHs migrate inwards under the influence of hydrodynamical torques unless they encounter a region where the torque flips sign. At these migration traps, BHs accumulate and merge via dynamical or gas-assisted interactions, producing high-frequency LIGO/Virgo/KAGRA (LVK) gravitational wave (GW) sources and potentially cutting off the supply of extreme mass ratio inspirals that would otherwise make low-frequency, LISA-band GWs. In this paper, we study the interplay between different types of migration torques, focusing especially on the ‘thermal torques’ generated by the thermal response of the AGN to embedded stellar-mass BHs that accrete through their own mini-discs. In contrast to previous work, we find that Type I torques cannot produce migration traps on their own, but thermal torques often do, particularly in low-mass AGN. The migration traps produced by thermal torques exist at much larger distances (∼103−5 gravitational radii) than do previously identified Type I traps, carrying implications for GW populations at multiple frequencies. Finally, we identify a bifurcation of AGN discs into two regimes: migration traps exist below a critical AGN luminosity, and do not at higher luminosities. This critical luminosity is fit as $\log _{10} L_{\rm AGN}^c = 45 {\!-\!} 0.32 \log _{10}{(\alpha /0.01)}$ where α is the Shakura–Sunyaev viscosity parameter, a range compatible with recent claims that LVK GWs are not preferentially associated with high-luminosity AGN.

A star that approaches a supermassive black hole (SMBH) on a circular extreme mass ratio inspiral (EMRI) can undergo Roche lobe overflow (RLOF), resulting in a phase of long-lived mass transfer onto the SMBH. If the interval separating consecutive EMRIs is less than the mass-transfer timescale driven by gravitational wave emission (typically ∼1–10 Myr), the semimajor axes of the two stars will approach each another on scales of ≲ hundreds to thousands of gravitational radii. Close flybys tidally strip gas from one or both RLOFing stars, briefly enhancing the mass-transfer rate onto the SMBH and giving rise to a flare of transient X-ray emission. If both stars reside in a common orbital plane, these close interactions will repeat on a timescale as short as hours, generating a periodic series of flares with properties (amplitudes, timescales, sources lifetimes) remarkably similar to the “quasi-periodic eruptions” (QPEs) recently observed from galactic nuclei hosting low-mass SMBHs. A cessation of QPE activity is predicted on a timescale of months to years, due to nodal precession of the EMRI orbits out of alignment by the SMBH spin. Channels for generating the requisite coplanar EMRIs include the tidal separation of binaries (Hills mechanism) or Type I inward migration through a gaseous AGN disk. Alternative stellar dynamical scenarios for QPEs, that invoke single stellar EMRIs on an eccentric orbit undergoing a runaway sequence of RLOF events, are strongly disfavored by formation rate constraints.