Leave-on-out is a special case of cross-validation where the number of folds equals the number of instances. Thus, models are always evaluated on one instance and trained on all others.
Leave-one-out is deterministic, bias-free, and does not require repeats or stratification. However, it is very computationally intensive and thus only advised for small data sets.
For leave-one-out, OpenML does not provide a train-test split file, but does require that the uploaded predictions are labeled with the row id of the test instance, so that the results can be properly evaluated and aggregated. OpenML stores both the per fold/repeat results and the aggregated scores.