We analyse star formation in the nuclei of 9 Seyfert galaxies at spatial resolutions down to 0.085arcsec, corresponding to length scales of less than 10pc in some objects. Our data were taken mostly with the near infrared adaptive optics integral field spectrograph SINFONI. The stellar light profiles typically have size scales of a few tens of parsecs. In two cases there is unambiguous kinematic evidence for stellar disks on these scales. In the nuclear regions there appear to have been recent - but no longer active - starbursts in the last 10-300Myr. The stellar luminosity is less than a few percent of the AGN in the central 10pc, whereas on kiloparsec scales the luminosities are comparable. The surface stellar luminosity density follows a similar trend in all the objects, increasing steadily at smaller radii up to 10^{13}L_sun/kpc^2 in the central few parsecs, where the mass surface density exceeds 10^4M_sun/pc^2. The intense starbursts were probably Eddington limited and hence inevitably short-lived, implying that the starbursts occur in multiple short bursts. The data hint at a delay of 50--100Myr between the onset of star formation and subsequent fuelling of the black hole. We discuss whether this may be a consequence of the role that stellar ejecta could play in fuelling the black hole. While a significant mass is ejected by OB winds and supernovae, their high velocity means that very little of it can be accreted. On the other hand winds from AGB stars ultimately dominate the total mass loss, and they can also be accreted very efficiently because of their slow speeds.
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