  We present a catalog of central engine properties, i.e., black hole mass
(mbh) and accretion luminosity (ld), for a sample of 1077 blazars detected with
the Fermi~Large Area Telescope. This includes broad emission line systems and
blazars whose optical spectra lack emission lines but dominated by the
absorption features arising from the host galaxy. The average mbh for the
sample is $\langle \log~M_{{\rm BH,all}~msun} \rangle=8.60$ and there are
evidences suggesting the association of more massive black holes with
absorption line systems. Our results indicate a bi-modality of ld~in Eddington
units (ld/ledd) with broad line objects tend to have a higher accretion rate
(ld/ledd$>$0.01). We have found that ld/ledd and Compton dominance (CD, the
ratio of the inverse Compton to synchrotron peak luminosities) are positively
correlated at $>$5$\sigma$ confidence level, suggesting that the latter can be
used to reveal the state of accretion in blazars. Based on this result, we
propose a CD based classification scheme. Sources with CD$>$1 can be classified
as High-Compton Dominated or HCD blazars, whereas, that with CD$\lesssim$1 are
Low-Compton Dominated (LCD) objects. This scheme is analogous to that based on
the mass accretion rate proposed in the literature, however, it overcomes the
limitation imposed by the difficulty in measuring ld and mbh for objects with
quasi-featureless spectra. We conclude that the overall physical properties of
Fermi blazars are likely to be controlled by the accretion rate in Eddington
units. The catalog is made public at http://www.ucm.es/blazars/engines and
Zenodo.

High Energy Astrophysical Phenomena;Astrophysics of Galaxies