  With Hubble Space Telescope imaging, we investigate the progenitor population
and formation mechanisms of the intracluster light (ICL) for 23 galaxy groups
and clusters ranging from 3$\times10^{13}<$M$_{500,c}$
[M$_\odot$]$<9\times10^{14}$ at 0.29$<$z$<$0.89. The color gradients of the
BCG+ICL become bluer with increasing radius out to 53-100 kpc for all but one
system, suggesting that violent relaxation after major mergers with the BCG
cannot be the dominant source of ICL. For clusters the BCG+ICL luminosity at
r$<$100 kpc (0.08-0.13 r$_{500,c}$) is 1.2-3.5$\times 10^{12}$L$_\odot$; for
the groups, BCG+ICL luminosities within 100 kpc (0.17-0.23 r$_{500,c}$) range
between 0.7-1.3$\times 10^{12}$ L$_\odot$. The BCG+ICL stellar mass in the
inner 100 kpc increases with total cluster mass as
M$_\bigstar\propto$M$_{500,c}$$^{0.37\pm0.05}$. This steep slope implies that
the BCG+ICL is a higher fraction of the total mass in groups than in clusters.
The BCG+ICL luminosities and stellar masses are too large for the ICL stars to
come from the dissolution of dwarf galaxies alone, implying instead that the
ICL grows from the stripping of more massive galaxies. Using the colors of
cluster members from the CLASH sample, we place conservative lower limits on
the luminosities of galaxies from which the ICL could originate. We find that
at 10 kpc the ICL has a color similar to massive, passive cluster galaxies
($>10^{11.6}$ M$_\odot$), while by 100 kpc this colour is equivalent to that of
a 10$^{10}$ M$_\odot$ galaxy. Additionally, we find 75% of the total BCG+ICL
luminosity is consistent in color of galaxies with L$>$0.2 L$_*$
(log(M$_\bigstar$[M$_\odot$])$>$10.4), assuming conservatively that these
galaxies are completely disrupted. We conclude that tidal stripping of massive
galaxies is the likely source of the intracluster light from 10-100 kpc
(0.008-0.23 r$_{500,c}$) for galaxy groups and clusters.
