I think you're no longer a kiddie host when:
a) You don't switch your host every other month (we have people switch from us, somewhere else back to use, somewhere else then want to come back to us so we just say no)
b) You realise that you're in this to make a living and not just enough money to buy a cd at the end of the month (if that)
c) When you realise that what other hosts say is irrelivant but you instead spend your time developing your business
I also think there's lots of other things which can help boost the professionalism of a company but do not necessarily relate to if the host is considered "kiddie". Although I find that the prices these kiddie hosts charge are causing issues as people will go "Why won't you do unlimited everything VPS for $2/month XYZ.com is!!!1"