  We present the second public data release (DR) of the VISTA EXtension to
Auxiliary Surveys (VEXAS), where we classify objects into stars, galaxies and
quasars based on an ensemble of machine learning algorithms. The aim of VEXAS
is to build the widest multi-wavelength catalogue, providing reference
magnitudes, colours and morphological information for a large number of
scientific uses. We apply an ensemble of 32 different machine learning models,
based on three different algorithms and on different magnitude sets, training
samples and classification problems on the three VEXAS DR1 optical+infrared
(IR) tables. The tables were created in DR1 cross-matching VISTA near-IR data
with 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 (415 628
unique objects), based on the combination of 6 different spectroscopic surveys
that we use for training. We develop feature imputation to classify also
objects for which magnitudes in one or more bands are missing. We classify in
total ~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 $p_{\rm class}\ge 0.7$ ($p_{\rm
class}\ge 0.9$). The density of high-confidence extragalactic objects varies
strongly with the survey depth: at $p_{\rm class}\ge 0.7$, there are
111/deg$^2$ quasars in the VEXAS-DESW footprint and 103/deg$^2$ in the
VEXAS-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 needed
for the SM footprint that is not already covered by DESW and PSW.
