We explore several ways to dissect brightest cluster galaxies (BCGs) and their surrounding intracluster light (ICL) using a surface brightness (SB) cut, a luminosity cut, excess light above a de Vaucouleurs profile, or a double Sersic decomposition. Assuming that all light above M{<}-21.85g'mag is attributable to the ICL, we find that an average fraction of f_ICL_^MT^=71+/-22% of all diffuse light centered on the BCG belongs to the ICL. Likewise, if we assume that all light fainter than SB>27g'mag/arcsec^2^ belongs to the ICL, the average ICL fraction is f_ICL_^SB27^=34+/-19% . After fitting a de Vaucouleurs profile to the inner parts of the SB profile, we detect excess light at large radii, corresponding to an average ICL fraction of f_ICL_^DV^=48+/-20% . Finally, by decomposing the SB profile into two Sersic functions, we find an average ICL fraction of f_ICL_^Sx^=52+/-21% associated with the outer Sersic component. Our measured ICL and BCG+ICL luminosities agree well with predictions from high-resolution simulations where the outer Sersic component traces the unrelaxed, accreted stellar material. BCG and ICL properties defined in this way are correlated with cluster parameters to study the coevolution of BCGs, ICL, and their host clusters. We find positive correlations between BCG+ICL brightness and cluster mass, cluster velocity dispersion, cluster radius, and integrated satellite brightness, confirming that BCG/ICL growth is indeed coupled with cluster growth. On average, the ICL is better aligned than the BCG with the host cluster in terms of position angle, ellipticity, and centering. That makes it a potential dark-matter tracer.