We have completed two years of photometric and spectroscopic monitoring of a large number of active galactic nuclei (AGNs) with very high accretion rates. In this paper, we report on the result of the second phase of the campaign, during 2013-2014, and the measurements of five new Hβ time lags out of eight monitored AGNs. All five objects were identified as super-Eddington accreting massive black holes (SEAMBHs). The highest measured accretion rates for the objects in this campaign areṀ 200, wherė M =Ṁ • /L Edd c −2 ,Ṁ • is the mass accretion rates, L Edd is the Eddington luminosity and c is the speed of light. We find that the Hβ time lags in SEAMBHs are significantly shorter than those measured in sub-Eddington AGNs, and the deviations increase with increasing accretion rates. Thus, the relationship between broad-line region size (R Hβ ) and optical luminosity at 5100Å, R Hβ − L 5100 , requires accretion rate as an additional parameter. We propose that much of the effect may be due to the strong anisotropy of the emitted slim-disk radiation. Scaling R Hβ by the gravitational radius of the black hole, we define a new radius-mass parameter (Y ) and show that it saturates at a critical accretion rate ofṀ c = 6 ∼ 30, indicating a transition from thin to slim accretion disk and a saturated luminosity of the slim disks. The parameter Y is a very useful probe -2for understanding the various types of accretion onto massive black holes. We briefly comment on implications to the general population of super-Eddington AGNs in the universe and applications to cosmology.

This is the third in a series of papers reporting on a large reverberation-mapping campaign aimed to study the properties of active galactic nuclei (AGNs) with high accretion rates. We present new results on the variability of the optical Fe II emission lines in 10 AGNs observed by the Yunnan Observatory 2.4 m telescope from2012 to2013. We detect statistically significant timelags, relative to the AGN continuum, in nine of the sources. This accurate measurement is achieved using a sophisticated spectral fitting scheme that allows for apparent flux variations of the host galaxy, and several narrowlines, due to the changing observing conditions. Six of the newly detected lags are indistinguishable from the Hβ lags measured in the same sources. Two are significantly longer and one is slightly shorter. Combining these findings with the Fe II lags reported in previous studies, we find an Fe II radius-luminosity relationship similar to the one for Hβ, although our sample by itself shows no clear correlation. The results support the idea that Fe II emission lines originate in photoionized gas, which, for the majority of the newly reported objects, is indistinguishable from the Hβ-emitting gas. We also present a tentative correlation between the lag and intensity of Fe II and Hβ and comment on its possible origin.