What is the mechanism generating the astrophysical jets?

The answer is: we still don't know. Even worse, we know "less than before". What we know now is that: " [...] the generation of highly relativistic outflows does not require properties that are unique to blackholes, such as an event horizon." said Fender et al., (15 Jan 2004) Nature 427, 222. It means that the famous Blanford-Znajek mechanism is in big trouble.

See also a pop-science coverage:

http://serwisy.gazeta.pl/nauka/1,34136,1876751.html