Okay, those three make me very confused. To my understanding だいぶ is used when it´s more than what you expected. 大体 should be more or less, but then where comes 大部分? And is 大体 a lesser percentage than ほとんど?
Thank you very much for your help.
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An adverb meaning "becoming more advanced (= grown, progressed, lapsed away...) than before", or if lacks the starting point it means "...than you/I expect", or simply "considerably". It doesn't tell anything about percentage.
Synonyms are 相当, かなり, ずいぶん etc.
An adverb but sometimes used noun-like, "almost all/complete", "almost every time/aspect" or "overall". You're right about "more or less" as in "more or less finished".
The difference with ほとんど is that:
Synonyms are おおむね, あらかた etc.
As you read, "(for) the great(est) part"; mostly noun, but also adverb. You can use this word only for something whose percentage is clear rather than subjective impression, and must tell "part of what (noun)" (and conversely, the other two are not going well with "of something").
だいぶ means "rather"and it is used as adjective and adverb.
大体、ほとんど means "almost" and they are used as noun and adverb.
大部分 means "for the most part" and "mostly", it is used as noun but sometimes used adverbially.
You choose these adverbs according to the situation.
For example, 私は図書館の本をだいぶ借りた(I rather borrowed books of a library).
私は図書館の本を大体(ほとんど)借りた(I almost borrowed books of a library).
私は図書館の本を大部分借りた(I mostly borrowed books of a library).
大体、ほとんど, 大部分 mean almost same.