Outlier detection (OD) has a vast literature as it finds numerous applications in environmental monitoring, cybersecurity, finance, and medicine to name a few. Being an inherently unsupervised task, model selection is a key bottleneck for OD (both algorithm and hyperparameter selection) without label supervision. There is a long list of techniques to choose from -- both classical algorithms and deep neural architectures -- and while several studies report their hyperparameter sensitivity, the literature is quite slim on unsupervised model selection -- limiting the effective use of OD in practice. In this paper we present FoMo-0D, for zero/0-shot OD exploring a transformative new direction that bypasses the hurdle of model selection altogether (!), thus breaking new ground. The fundamental idea behind FoMo-0D is the Prior-data Fitted Networks, recently introduced by Muller et al.(2022), which trains a Transformer model on a large body of synthetically generated data from a prior data distribution. In essence, FoMo-0D is a pretrained Foundation Model for zero/0-shot OD on tabular data, which can directly predict the (outlier/inlier) label of any test data at inference time, by merely a single forward pass -- making obsolete the need for choosing an algorithm/architecture, tuning its associated hyperparameters, and even training any model parameters when given a new OD dataset. Extensive experiments on 57 public benchmark datasets against 26 baseline methods show that FoMo-0D performs statistically no different from the top 2nd baseline, while significantly outperforming the majority of the baselines, with an average inference time of 7.7 ms per test sample.