Final answer:
Open star clusters ultimately disperse, as the stars within them exceed the escape velocity due to their own speeds or interactions with other stars or molecular clouds, not typically leading to the formation of a massive black hole or globular clusters.
Step-by-step explanation:
The ultimate fate of an open star cluster is that the stars within it will gradually disperse over time. This evolution is driven by several factors. In small open clusters, the speeds of stars can sometimes exceed the escape velocity, leading to their gradual 'evaporation' from the cluster. Additionally, close encounters between stars can impart enough velocity to individual stars to escape the cluster's gravitational pull. Another significant event that can lead to the cluster's disruption is a close encounter with a giant molecular cloud whose gravity can tear the cluster apart.
Over time, as stars follow their evolutionary paths, they will transform into various end stages like white dwarfs, neutron stars, or black holes. These end stages don't necessarily result in a single massive black hole, as the dynamic environment within dense clusters prevents the formation of an accretion disk around a forming black hole. Therefore, the assertion that open star clusters inevitably lead to the formation of a black hole or become globular clusters is incorrect. Instead, the dispersion of the cluster happens due to the reasons mentioned above.