A friend and I walked past a poster advertising BabiesRUs and the slogan was "Everything for baby". My friend said it's bad grammar and should include "your" or make "baby" into "babies". I disagreed but couldn't give a reasonable explanation as to why it is okay to omit the determiner in this case, but I'm still convinced it's perfectly reasonable, especially because it's advertising copy and doesn't necessarily have to conform to strict grammar. But even in everyday English, it seems perfectly correct to me.
Is it okay to omit the determiner in some cases and what are those cases?