First, the difference between ~면 and ~다면. * ~면: simple conditional. 시간 되면 알려줘 (Let me know if you have time). * ~다면: conditional with a greater hypothetical and/or formal sense. 시간 된다면 알려줘 (Let me know if you should have time - more indirect and polite). ~다면 comes from ~다고 한다면, where ~다고 is a quoting form and 한다 means 말하다(say) or 치다/가정하다(assume). So ~다면 is suitable for more unlikely or abstract ideas, or when you want to be more polite, whereas ~면 expresses a simple condition. There is no implication of tense in either phrase. Tense is determined by what comes before them, as in 네가 그걸 봤(으/다)면 (past), 네가 그걸 보면/본다면(present), and 네가 그걸 볼 거면/거라면 (future). As for ~ㄴ다면 vs ~다면, it has to do with the way verbs and adjectives diverge in some conjugation forms. ~다면 is actually nothing more than the canonical sentence ending form ~다 merged with the conditional form ~면. Using 되다(v) and 크다(a) as examples, the common present tense sentence endings are: 1 됩니다, 큽니다 - (formal, polite) 2 된다, 크다 - (formal, plain) *canonical 3 돼요, 커요 - (informal, polite) 4 돼, 커 - (informal, polite) Note that in (2), the verb 되다 acquires ㄴ for the conjugation but the adjective 크다 does not. This is an important distinction between verb and adjective conjugation, which also explains why there is ~ㄴ다면(v) and ~다면(a). For example: - 이 일을 못한다면 다른 걸 줄게 vs 이 일이 너무 어렵다면 다른 걸 줄게. (못하다(v)- > 못한다, 어렵다(a) doesn't change) - 기회가 다시 온다면 ... vs 기회가 다시 있다면 ... (오다(v) -> 온다면, 있다(a) doesn't change) One last thing to note is 이다, which is a special verb-particle (or "coupla", like "is" in "AA is BB") that takes its own conjugation form in some contexts. - 이게 마지막이다 (declarative) vs 이게 마지막이라면 (conditional). (neither 인다면 nor 이다면, but 이라면) - 네가 할 거라면 내가 도와 줄게. (거라면 is 것이다 + ~면 which becomes 것이라면 or its contraction 거라면) So for ~다면 form, there are verbs(~ㄴ다면), adjectives(~다면), and the special verb-like particle 이다(~(이)라면). But for ~면, there is no such difference - 하면(v), 크면(a), and (이)면.

I'm not posting this as an answer because I'm not 100% myself, but the way I understand it 다면 is more of an emphasis on "hypothetically". I commonly heard 만약에 시간이 된다면 as in, "Hypothetically, if you WERE to have time..." whereas "시간이 있으면" would be more of "If you have time" Like I said, not 100% myself but that's how I always interpreted it.