  Interstellar objects (ISOs), the parent population of 1I/Oumuamua and
2I/Borisov, are abundant in the interstellar medium of the Milky Way. This
means that the interstellar medium, including molecular cloud regions, has
three components: gas, dust, and ISOs. From the observational constraints for
the field density of ISOs drifting in the solar neighbourhood, we infer a
typical molecular cloud of 10 pc diameter contains some 10$^{18}$ ISOs. At
typical sizes ranging from hundreds of metres to tens of km, ISOs are entirely
decoupled from the gas dynamics in these molecular clouds. Here we address the
question of whether ISOs can follow the collapse of molecular clouds. We
perform low-resolution simulations of the collapse of molecular clouds
containing initially static ISO populations toward the point where stars form.
In this proof-of-principle study, we find that the interstellar objects
definitely follow the collapse of the gas -- and many become bound to the
new-forming numerical approximations to future stars (sinks). At minimum, 40\%
of all sinks have one or more ISO test particles gravitationally bound to them
for the initial ISO distributions tested here. This value corresponds to at
least $10^{10}$ actual interstellar objects being bound after three initial
free-fall times. Thus, ISOs are a relevant component of star formation. We find
that more massive sinks bind disproportionately large fractions of the initial
ISO population, implying competitive capture of ISOs. Sinks can also be
solitary, as their ISOs can become unbound again -- particularly if sinks are
ejected from the system. Emerging planetary systems will thus develop in
remarkably varied environments, ranging from solitary to richly populated with
bound ISOs.
