  We aim to constrain the sizes of the CO circumstellar envelopes (CSEs) of 16
S-type stars, along with an additional 7 and 4 CSEs of C-type and M-type AGB
stars, respectively. We map the emission from the CO J=2-1 and 3-2 lines
observed with the Atacama Compact Array (ACA) and its total power (TP)
antennas, and fit with a Gaussian distribution in the uv- and image planes for
ACA-only and TP observations, respectively. The major axis of the fitted
Gaussian for the CO(2-1) line data gives a first estimate of the size of the
CO-line-emitting CSE. We investigate possible signs of deviation from spherical
symmetry by analysing the line profiles, the results from visibility fitting,
and by investigating the deconvolved images. The sizes of the CO-line-emitting
CSEs of low-mass-loss-rate (low-MLR) S-stars fall between the sizes of the CSEs
of C-stars, which are larger, and those of M-stars, which are smaller, as
expected because of the differences in their respective CO abundances. The
sizes of the low-MLR S-type stars show no dependence on circumstellar density,
while a steeper density dependence is observed at high MLR. Furthermore, our
results show that the CO CSEs of most of the S-stars in our sample are
consistent with a spherically symmetric and smooth outflow. The CO envelope
sizes obtained in this paper will be used to constrain detailed radiative
transfer modelling to directly determine more accurate MLR estimates for the
stars in our sample. For several of our sources that present signs of deviation
from spherical symmetry, further high-resolution observations would be
necessary to investigate the nature of, and the physical processes behind,
these asymmetrical structures. This will provide further insight into the
mass-loss process and its related chemistry in S-type AGB stars.
