PHBoth are correct, under different circumstances.
- "Anytime" is an adverb, which can be used to answer a question such as "When can I come to see you?" The response could be "Anytime."
- "Any time" is a compound noun, where "time" is a noun and "any" is an adjective describing the noun "time." It could be used to answer a question such as "What time would be good to see you?" The response could be "Any time."
