We propose to study star formation (SF) in extreme environments in order to test to breaking point the many prescriptions that have been proposed that predict under which conditions SF occurs. In particular we will investigate (i) what sets the threshold for SF and (ii) what determines, once above this threshold, the rate of SF. So far, studies dedicated to this question have been based only on data of spiral and dwarf galaxies. We argue that in order to make progress, observations are needed of SF in extreme environments, such as intergalactic SF regions. We propose to study the relation between SF and SF rate (SFR), and the neutral (atomic and molecular) gas in a sample of 13 intergalactic SF regions, spanning a wide range of luminosities. All targets have a wealth of ancillary data, mainly obtained by us such as HI, CO, Halpha, and GALEX UV. Although the latter two are indicators of unobscured SF, we know that even in intergalactic SF regions there is dust and considerable extinction. It is therefore crucial to obtain MIPS 24 um maps to determine the total SF (obscured and unobscured). A modest 2.5 hrs total time spent on 13 targets is guaranteed to deliver a substantial return on investment in the form of a much improved understanding of the sufficient and necessary conditions for SF to take place.