Typically, they don't care much about standard measures of value, so long as earnings continue to rise rapidly. American Century Ultra is a good example of a growth fund. Managers of these funds look for stocks of growing companies selling at attractive prices. So a large-cap growth fund would look for stocks with rapid earnings growth among the nation's biggest companies. Lipper adds a fourth category, called multicap.
Some managers move up and down the capitalization spectrum, depending on market conditions.
It feels so good drowning in 10 feet of water rather than in 20 feet. But we can dream. That can be rather pointless, as you note. Funds advertise because they want your money, obviously. They argue that a larger fund means lower expenses, which means savings for the shareholder.