Abstract　 　　  

   What is the lifespan of these supermassive blackholes?  I will start with a general introduction of the existing methods of quasar-age estimations, then present our recent results on the proximity profiles in the spectra of z ≈ 3 quasars, where fluxes extend blueward of the He ii Ly  wavelength 304(1+z) A.  Based on the HST spectra of He II quasars collected over two decades, we find a large difference in the proximity-zone sizes  up to  20 Mpc in the source’s rest frame.  With further modeling, we should in principle be able to estimate the quasar ages from their proximity sizes. Several special interesting cases will be discussed.