We present a study of the Kreutz, Marsden, and Kracht comets observed by SOHO including photometric reductions and analysis, numerical modeling, and physical modeling. We analyze the results of our photometric study of more than 900 lightcurves of Kreutz comets observed by SOHO. We find that they do not have a bimodal distance of peak brightness as previously reported, but instead peak from 10.5-14 solar radii (prior to perihelion), suggesting there is a continuum of compositions rather than two distinct subpopulations. The lightcurves have two rates of brightening, typically ~r^-7.3 when first observed by SOHO then rapidly transitioning to ~r^-3.8 between 20-30 solar radii. It is unclear at what distance the steeper slope begins, but it likely does not extend much beyond the SOHO field of view. We derive nuclear sizes up to ~50 meters in radius for the SOHO observed comets, with a cumulative size distribution of N(>R)~R^-2.2 for comets larger than 5 meters in radius. This size distribution cannot explain the six largest members of the family seen from the ground, suggesting that either the family is not collisionally evolved or that the distribution is not uniform around the orbit. After correcting for the changing discovery circumstances, the flux of comets reaching perihelion has increased since 1996, and the increase is seen in comets of all sizes.

We consider the Marsden and Kracht comets together due to their apparent dynamical linkage. Seasonal effects of the viewing geometry make it impossible to build a characteristic lightcurve of either group. Many are seen to survive perihelion and most reach a peak brightness within ~6 hours of perihelion with no preference for peaks before or after perihelion. Most are barely above the detection threshold, and the largest is probably smaller than 30 meters in radius. Our dynamical simulations suggest that the orbital distribution of the Kracht group can be produced by low velocity fragmentation events and close approaches to Jupiter over the last 50-250 years. We construct fragmentation trees for the Marsden and Kracht groups and predict that 7-8 comets in each group may be visible on their next perihelion passage.