  Numerical simulations have shown the occurence of a scenario termed
''super-competitive accretion'', a term that describes a situation where only
the central few objects grow supermassive while a larger number of stars
compete for the reservoir, with significant accretion flows of $\gtrsim0.1$
M$_\odot$ yr$^{-1}$. This scenario particularly implies that the presence of
fragmentation will not necessarily impeed the formation of a central massive
object. We here explore this phenomenon using analytical estimates for growth
via collisions and accretion, considering accretion due to self-gravity as well
as Bondi-Hoyle accretion. Particularly, we explore under what conditions the
accretion onto the central massive object breaks down, and derive a criterion
that depends on the mass of the most massive object and the mass in fragments.
For compact clusters with sizes about $0.1$~pc, we further find that the mass
growth by collisions is comparable to the growth via accretion. Our results are
validated through the comparison with numerical simulations, and we overall
conclude that super-competitive accretion is a valid mechanism for the
formation of very massive objects in the early Universe.
