  Models aiming to explain the formation of massive black hole seeds, and in
particular the direct collapse scenario, face substantial difficulties. These
are rooted in rather ad hoc and fine-tuned initial conditions, such as the
simultaneous requirements of extremely low metallicities and strong radiation
backgrounds. Here we explore a modification of such scenarios where a massive
primordial star cluster is initially produced. Subsequent stellar collisions
give rise to the formation of massive (10^4 - 10^5 solar mass) objects. Our
calculations demonstrate that the interplay between stellar dynamics, gas
accretion and protostellar evolution is particularly relevant. Gas accretion
onto the protostars enhances their radii, resulting in an enhanced collisional
cross section. We show that the fraction of collisions can increase from 0.1-1%
of the initial population to about 10% when compared to gas-free models or
models of protostellar clusters in the local Universe. We conclude that very
massive objects can form in spite of initial fragmentation, making the first
massive protostellar clusters viable candidate birth places for observed
supermassive black holes.
