Vanguard by far has largest number of funds leading their respective categories in assets under management, as seen in table below. At 44, that’s almost 30% of the 155 categories Lipper tracks.
Pulling on this one a bit more … Vanguard has 178 funds in 81 categories, so with 44 of its funds leading their categories in AUM, Vanguard leads more that half of the categories it “competes” in! Wow.