  Observations indicate that young massive star clusters in spiral and dwarf
galaxies follow a relation between luminosity of the brightest young cluster
and the star-formation rate (SFR) of the host galaxy, in the sense that higher
SFRs lead to the formation of brighter clusters. Assuming that the empirical
relation between maximum cluster luminosity and SFR reflects an underlying
similar relation between maximum cluster mass (M_ecl,max) and SFR, we compare
the resulting SFR(M_ecl,max) relation with different theoretical models. The
empirical correlation is found to suggest that individual star clusters form on
a free-fall time-scale with their pre-cluster molecular-cloud-core radii
typically being a few pc independent of mass. The cloud cores contract by
factors of 5 to 10 while building-up the embedded cluster. A theoretical
SFR(M_ecl,max) relation in very good agreement with the empirical correlation
is obtained if the cluster mass function of a young population has a Salpeter
exponent beta approx. 2.35 and if this cluster population forms within a
characteristic time-scale of a few-10 Myr. This short time-scale can be
understood if the inter-stellar medium is pressurised thus precipitating rapid
local fragmentation and collapse on a galactic scale. Such triggered star
formation on a galactic scale is observed to occur in interacting galaxies.
With a global SFR of 3-5 Msol/yr the Milky Way appears to lie on the empirical
SFR(M_ecl,max) relation, given the recent detections of very young clusters
with masses near 10^5 Msol in the Galactic disk. The observed properties of the
stellar population of very massive young clusters suggests that there may exist
a fundamental maximum cluster mass, 10^6 < M_ecl,max*/Msol < 10^7.
