This paper investigates the design and optimization of a thin acoustic metamaterial for broadband sound absorption using acoustic black hole (ABH) profiles. The metamaterial, known as the multi-pancake absorber, consists of periodically arranged thin annular cavities separated by plates and connected by a main pore. The study focuses on geometric variations of the main pore, specifically ABH profiles with a gradually decreasing radius, to achieve broadband absorption. An analytical model based on the transfer matrix approach and lumped elements is proposed to predict the acoustic properties. The model is validated through thermo-visco-acoustic finite element simulations and impedance tube measurements. The research highlights the importance of balancing losses among the modes to achieve perfect absorption at multiple peaks. The complex frequency plane representation is used to analyze the influence of the main pore radius at the entrance and backing of the sample. The study finds that a decreasing main pore profile can enhance the acoustic performance by introducing noticeable local resonances, leading to a more pronounced clustering effect and increased visibility of absorption peaks. Non-linear decreasing profiles are also explored to accentuate losses and achieve absorption peaks of similar amplitude. The paper concludes with the design of broadband ABH profiles that optimize the balance of losses and achieve high absorption coefficients across a broad frequency range. The insights gained from the study provide a foundation for further improvements in the design of thin, broadband acoustic absorbers.This paper investigates the design and optimization of a thin acoustic metamaterial for broadband sound absorption using acoustic black hole (ABH) profiles. The metamaterial, known as the multi-pancake absorber, consists of periodically arranged thin annular cavities separated by plates and connected by a main pore. The study focuses on geometric variations of the main pore, specifically ABH profiles with a gradually decreasing radius, to achieve broadband absorption. An analytical model based on the transfer matrix approach and lumped elements is proposed to predict the acoustic properties. The model is validated through thermo-visco-acoustic finite element simulations and impedance tube measurements. The research highlights the importance of balancing losses among the modes to achieve perfect absorption at multiple peaks. The complex frequency plane representation is used to analyze the influence of the main pore radius at the entrance and backing of the sample. The study finds that a decreasing main pore profile can enhance the acoustic performance by introducing noticeable local resonances, leading to a more pronounced clustering effect and increased visibility of absorption peaks. Non-linear decreasing profiles are also explored to accentuate losses and achieve absorption peaks of similar amplitude. The paper concludes with the design of broadband ABH profiles that optimize the balance of losses and achieve high absorption coefficients across a broad frequency range. The insights gained from the study provide a foundation for further improvements in the design of thin, broadband acoustic absorbers.