  The formation of massive objects via gravitational collapse is relevant both
for explaining the origin of the first supermassive black holes and in the
context of massive star formation. Here, we analyze simulations of the
formation of massive objects pursued by different groups and in various
environments, concerning the formation of supermassive black holes, primordial
stars, as well as present-day massive stars. We focus particularly on the
regime of small virial parameters, i.e., low ratios of the initial kinetic to
gravitational energy, low to moderate Mach numbers, and the phase before
feedback is very efficient. We compare the outcomes of collapse under different
conditions using dimensionless parameters, particularly the star formation
efficiency \epsilon_*, the fraction f_* of mass in the most massive object
relative to the total stellar mass, and the fraction f_{\rm tot} of mass of the
most massive object as a function of the total mass. We find that in all
simulations analyzed here, f_{\rm tot} increases as a function of \epsilon_*,
although the steepness of the increase depends on the environment. The relation
between f_* and \epsilon_* is found to be more complex and also strongly
depends on the number of protostars present at the beginning of the
simulations. We show that a collision parameter, estimated as the ratio of the
system size divided by the typical collision length, allows us to approximately
characterize whether collisions will be important. We analyze the statistical
correlation between the dimensionless quantities using the Spearman coefficient
and confirm via a machine learning analysis that good predictions of f_* can be
obtained from \epsilon_* together with a rough estimate of the collision
parameter. This suggests that a good estimate of the mass of the most massive
object can be obtained once the maximum efficiency for a given environment is
known.
