  We present a model for the concurrent formation of globular clusters (GCs)
and supermassive stars (SMSs, $>10^3\,{\rm M}_\odot$) to address the origin of
the HeCNONaMgAl abundance anomalies in GCs. GCs form in converging gas flows
and accumulate low-angular momentum gas, which accretes onto protostars. This
leads to an adiabatic contraction of the cluster and an increase of the stellar
collision rate. A SMS can form via runaway collisions if the cluster reaches
sufficiently high density before two-body relaxation halts the contraction.
This condition is met if the number of stars $\gtrsim10^6$ and the gas
accretion rate $\gtrsim10^5\,{\rm M}_\odot$/Myr, reminiscent of GC formation in
high gas-density environments, such as -- but not restricted to -- the early
Universe. The strong SMS wind mixes with the inflowing pristine gas, such that
the protostars accrete diluted hot-hydrogen burning yields of the SMS. Because
of continuous rejuvenation, the amount of processed material liberated by the
SMS can be an order of magnitude higher than its maximum mass. This
`conveyor-belt' production of hot-hydrogen burning products provides a solution
to the mass budget problem that plagues other scenarios. Additionally, the
liberated material is mildly enriched in helium and relatively rich in other
hot-hydrogen burning products, in agreement with abundances of GCs today.
Finally, we find a super-linear scaling between the amount of processed
material and cluster mass, providing an explanation for the observed increase
of the fraction of processed material with GC mass. We discuss open questions
of this new GC enrichment scenario and propose observational tests.
