We present a new modeling of the X-ray luminosity function (XLF) of active galactic nuclei (AGNs) out to z ∼ 3, dissecting the contributions of main-sequence (MS) and starburst (SB) galaxies. For each galaxy population, we convolved the observed galaxy stellar mass (M_⋆) function with a grid of M_⋆-independent Eddington ratio (λ_EDD) distributions, normalized via empirical black hole accretion rate (BHAR) to star formation rate (SFR) relations. Our simple approach yields an excellent agreement with the observed XLF since z ∼ 3. We find that the redshift evolution of the observed XLF can only be reproduced through an intrinsic flattening of the λ_EDD distribution and with a positive shift of the break λ*, consistent with an antihierarchical behavior. The AGN accretion history is predominantly made by massive (10¹⁰ < M_⋆ < 10¹¹ M_⊙) MS galaxies, while SB-driven BH accretion, possibly associated with galaxy mergers, becomes dominant only in bright quasars, at log(L_X/erg s^-1) > 44.36 + 1.28 × (1 + z). We infer that the probability of finding highly accreting (λ_EDD > 10%) AGNs significantly increases with redshift, from 0.4% (3.0%) at z = 0.5%-6.5% (15.3%) at z = 3 for MS (SB) galaxies, implying a longer AGN duty cycle in the early universe. Our results strongly favor a M_⋆-dependent ratio between BHAR and SFR, as BHAR/SFR ∝ M_\star^{0.73[+0.22,-0.29]}, supporting a nonlinear BH buildup relative to the host. Finally, this framework opens potential questions on super-Eddington BH accretion and different λ_EDD prescriptions for understanding the cosmic BH mass assembly.