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We present the second public data release (DR) of the VISTA EXtension toAuxiliary Surveys (VEXAS), where we classify objects into stars, galaxies andquasars based on an ensemble of machine learning algorithms. The aim of VEXASis to build the widest multi-wavelength catalogue, providing referencemagnitudes, colours and morphological information for a large number ofscientific uses. We apply an ensemble of 32 different machine learning models,based on three different algorithms and on different magnitude sets, trainingsamples and classification problems on the three VEXAS DR1 optical+infrared(IR) tables. The tables were created in DR1 cross-matching VISTA near-IR datawith WISE far-IR data and with optical magnitudes from the Dark Energy Survey(VEXAS-DESW), the Sky Mapper Survey (VEXAS-SMW), and the PanSTARRS (VEXAS-PSW).We assemble a large table of spectroscopically confirmed objects (415 628unique objects), based on the combination of 6 different spectroscopic surveysthat we use for training. We develop feature imputation to classify alsoobjects for which magnitudes in one or more bands are missing. We classify intotal ~90 million objects in the Southern Hemisphere. Among these,~62.9M(~52.6M) are classified as 'high confidence' ('secure') stars, ~920k (~750k) as'high confidence' ('secure') quasars and ~34.8M (~34.1M) as 'high confidence'('secure') galaxies, with probabilities $p_{\rm class}\ge 0.7$ ($p_{\rmclass}\ge 0.9$). The density of high-confidence extragalactic objects variesstrongly with the survey depth: at $p_{\rm class}\ge 0.7$, there are111/deg$^2$ quasars in the VEXAS-DESW footprint and 103/deg$^2$ in theVEXAS-PSW footprint, while only 10.7/deg$^2$ in the VEXAS-SM footprint.Improved depth in the midIR and coverage in the optical and nearIR are neededfor the SM footprint that is not already covered by DESW and PSW.

VEXAS: VISTA EXtension to Auxiliary Surveys -- Data Release 2: Machine-learning based classification of sources in the Southern Hemisphere