Alpha Centauri AB system contains the closest Sun-like stars to the Sun, by a large margin (factor of 2.4). This confers considerable advantages to the detection and characterization of planets around them, especially with direct imaging and astrometry. In particular, a planet around Alpha Centauri A or B would appear at least 6x brighter, and at least 2.4x more separated from its host star, than a similar planet around any other Sun-like star. Further, one of the stars (B) is a K-dwarf, where the planet-star flux ratio for a potentially habitable planet can be as high as 1e-9 (at least in Gibbous phase), while still appearing at a relatively large separation angle of 0.4" from its host star, due to the system's unusual proximity to us. However, any effort to search for planets around Alpha Centauri AB must face several critical questions: whether planets can exist in the system, what their expected occurrence rate is, and what kinds of planets are possible and/or likely. In particular, whether potentially habitable planets are possible, and what their occurrence rate is. This paper combines the current knowledge of occurrence rates, corrections for binarity specific to Alpha Centauri, limits from RV non-detections, and dynamical stability simulations, in order to answer these questions. We also consider how the possible Alpha Centauri Ab planet candidate announced by the NEAR project might affect the occurrence rates and types of planets in the system. In particular, we first use and compare two Kepler-based occurrence rates as our baseline: Dulz et al. 2020 and Bryson et al. 2021 (the former was used for LUVOIR and HabEx yield estimation, and the latter was the final occurrence rate paper by the Kepler mission team). We then apply the binarity corrections from Moe et al. 2021 to account for Alpha Centauri AB binarity. Finally, we apply constraints on planet mass-period space from RV non-detections (Zhao et al. 2018), and from dynamical stability limits (Quarles and Lissauer 2016, and others) to obtain the occurrence rate distribution for each of the two stars. We use the resulting occurrence rate distribution, and its uncertainties, to obtain the occurrence rates and uncertainties for different types of planets, including potentially habitable ones, as well as the overall occurrence rate. We also identify the likeliest planets that may exist in the system, and assess the probability of no planets at all.