  There is a maximum for the gravity of a black hole in the vertical direction
in the accretion disc. Outflows may probably be driven from the disc if the
radiation flux of the disc is greater than a critical value corresponding to
the maximal vertical gravity. We find that outflows are driven by the radiation
force from the disc if the accretion rate is greater than the Eddington rate.
The radiation of the disc is therefore limited by such outflows. The disc
luminosity, L=L_Edd\propto ln mdot, at large-mdot cases. The Eddington ratio of
the disc is ~3 for mdot~100, which is significantly lower than that of a
conventional slim disc without outflows. This implies that the emission from
some ultra-luminous X-ray sources with highly super Eddington luminosity should
be Doppler beamed, or intermediate mass black holes are in these sources
instead of stellar mass black holes. The spectra of the discs with outflows are
saturated in the high frequency end provided mdot>2. We suggest that the
saturated emission can be observed to estimate the masses of the black holes
accreting at high rates, such as the narrow-line Seyfert galaxies, with the
model calculations. The rate of the mass accreted by the black hole is always
around the Eddington rate even if the mass accretion rate at the outer radius
is very high, because most of the gas is removed into the outflows. This
implies that the luminous quasars at high redshifts z>6 should have grown up
through persistent accretion at a rate close to the Eddington rate.
