  We present a detailed model of an extreme slim disk (ESD) with a hot corona
around a massive black hole with dimensionless accretion rate $\dotm$ in the
range $2.5\ll \dotm\leq 100$. We assume that a fraction $f$ of the
gravitational energy is released in the hot corona and the rest is released in
the ESD. The energy equation of the ESD is dominated by advection and the
spectrum shows a broad ``hump'' caused by saturated Comptonization with
monochromatic luminosity given by $\nu L_{\nu}\propto \nu^0$. This relationship
enables us to estimate the black hole mass from the ESD luminosity. The
spectrum of the hot corona is sensitive to the parameter $f\dotM$ and the
viscosity and shows a Comptonized power-law with a high-energy cutoff. The
model is used to explain the spectral properties of narrow line Seyfert 1
galaxies (NLS1s). In particular, it can explain the spectrum of extreme NLS1s
like NLS1 RE J1034+396. Our spectral estimate of the black hole mass in this
source is in good agreement with the mass obtained by applying the
reververation mapping correlation. We also examine the Eddington ratios in a
large NLS1 sample and find that most objects show super-Eddington accretion
rates. We argue that soft X-ray humps in NLS1s are natural consequences of
super-Eddington accretion in such objects.
