The detailed processes leading to star formation at large scales in a galaxy disk or in the nucleus are still not well known. Many physical mechanisms can explain observations: gravitational instabilities, cloud-cloud collisions, density-wave and radial flows, propagating star-formation, galaxy interactions...
Empirical laws like the "global" Schmidt law do not help in disentangling the role of all these physical phenomena. Moreover, a "local" Schmidt law is still an unconfirmed paradigm, since there is no tight correlation between local gas density and SFR density.
The main factor towards giant starbursts is the quick flow of gas in a concentrated region in a short enough time-scale (< 10 Myr), to beat the stellar feedback processes. This can only be provided by gravity torques in gaseous disks (due for instance to galaxy interactions, that trigger bars, etc...)
This mechanism might be preponderant only at late Hubble times, when galaxies are massive, with stabilising bulges. At earlier times (z > 1), galaxies are less evolved and less concentrated; they are not stabilised against gravitational instabilities; those can be violent, triggering spontaneous bursts, with a chaotic appearance, accounting for the irregular and knotty images observed at high redshift.
Starbursts and AGN are often observed in symbiosis in galaxies, they are not only fed by the same mechanisms, but sometimes regulate each other. The observations at high redshift help to get insight in the time evolution of both, leading to parallel growth of bulges and supermassive black holes. Dark haloes forming earlier are denser, explaining why supermassive black holes forming earlier are more massive (Haehnelt & Kauffmann 2000).
Evolutionary cosmological models (N-body simulations + semi-analytical experiments) succeed to some extent to reproduce observations: they use a local Schmidt law for star formation
and introduce schematically the stellar feedback, by yielding energy at each star formation to increase the bulk motion of the gas. Simulations retrieve rather well the slope of the Tully-Fischer relation, which appears to be not very sensitive to SF prescriptions (e.g. Steinmetz & Navarro 2000). But there is a big problem to retrieve the zero point: at a given rotational velocity, model galaxies are 2 magnitude dimmer than observed galaxies. The problem is now well identified, the dark matter is too much concentrated in the models, and there is not enough baryons in the central regions of a galaxy disk. This has also been remarked in fitting rotation curves and in particular of dwarf irregulars, that are dominated by dark matter. This is independent of cosmological parameters (CDM, or CDM), although the efficiency to transform baryons into stars is much higher in CDM (~ 100%) than in CDM (~ 40%) (Navarro & Steinmetz 2000).
I am very grateful to Johan Knappen and collaborators for the organisation of such a pleasant and fruitful conference, to their sponsors and the CNRS for their financial help.