Real-world analytics hinges on tabular data, yet prevailing learners face a triple bind: tree ensembles excel on fixed schemas but cannot generalize to new columns, neural nets learn rich features yet overfit small tables, and recent transfer approaches falter when schemas diverge. We tackle these limitations with GTab, a Gradient-Boosting Bipartite Graph Neural Network that marries decision-tree residual refinement with self-supervised graph representation learning. GTab maps each table to an instance-feature bipartite graph, where a GNN, optimised jointly with contrastive, clustering, and reconstruction objectives, captures feature-feature, instance-instance, and cross-type relations. Boosted trees ingest the GNN's gradients, correcting residual errors and injecting the strong inductive bias of split-based models. Building on this backbone, we introduce three variants: E-GTab ensembles multiple overlapping feature sub-graphs for robust classic prediction; I-GTab inductively attaches unseen feature nodes, enabling feature-incremental inference without retraining; and T-GTab pre-trains on a source schema and lightly fine-tunes on a target schema to achieve zero-shot and transfer learning across heterogeneous tables. Across 20 public benchmarks and five clinical trials, GTab consistently ranks first: it outperforms tree, neural, and graph baselines on static tasks, surpasses prior art (and an oracle) when half the test-time columns are unseen, and delivers higher AUC than the leading transformer baseline in both cross-dataset and zero-shot transfer – all with a unified architecture. GTab thus offers a principled, scalable, and adaptable solution to holistic tabular data prediction, bridging the gap between classic ensembles and modern self-supervised representation learning.