Surface-based cortical analysis is useful in many applications as it is a natural way to model the highly folded structure of the cerebral cortex, allowing quantities such as curvature and thickness to be easily calculated. Existing deep learning (DL) methods have focused on 1x1x1 mm3 T1-weighted (T1w) scans, thus replicating classical pipelines. Here we present a neural network that is trained exclusively on synthetic scans with random contrast and resolution. Consequently, it can be applied to almost any kind of magnetic resonance imaging (MRI) scan. In addition, our model provides vertex-wise uncertainty estimates of the predicted surface as well as a spherical registration to fsaverage space. Our model performs on par with other state-of-the-art DL methods on 1x1x1 mm3 T1w scans and outperforms the only other method capable of estimating cortical surfaces from low resolution, non-T1w scans. The predicted uncertainty, moreover, correlates with overall scan quality on low resolution scans and highlights areas of poor surface reconstruction on 1x1x1 mm3 T1w scans, suggesting that it can be used for quality control. Finally, the predicted spherical registrations prove comparable to other DL and classical registration methods. These qualities, when combined with the fast inference time, will provide the ability to analyze large, existing databases of clinical MRI scans, with the potential for finding disease-specific patterns that would otherwise be infeasible in a research setting.

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