I understand that cD galaxies, very large and bright galaxies, have more globular clusters than other galaxies. For example, by calculating the specific frequency for a cD galaxy, the number is approximately 18.6 in contrast to a M31-like galaxy with 0.73. What I do not understand is why the amount of globular clusters is so high in the cD galaxy. I do not know if a possible reason is that the number of globular clusters increases with luminosity and as cD galaxies have high surface brightness in central regions, the formation of globular clusters is more effective.
I cannot claim to be up-to-date with the literature on this topic, but one hypothesis is that the high specific frequencies in cD galaxies comes from the combination of the fact that they have larger mass to light ratios, so for a fixed number of clusters per units stellar mass, they have more clusters per unit luminosity, and that their reservoir of gas, which is substantially larger than for other galaxy types, allows them to form many more clusters at early times. This is discussed in some detail in/around this section of Harris (1999).