[verb た-form] + 末(に) [noun] + の + 末(に) [verb た-form] + 末の + [noun] [noun] + の + 末の + [noun]
た末 and の末 mean "after (a long process of)": the result came only at the end of a lot of thought, effort or trouble. 末 follows a verb's た-form, or a noun with の. The に after it is optional.
The noun before の末 is itself a process: ぎろん議論, くろう苦労, どりょく努力, こうしょう交渉. The second half is what that process finally led to, and it is usually in the past.
To describe a noun that follows, 末 takes の after it, and that noun is the result: a decision, a success, a choice.
The process has to be long or hard. For something quick and ordinary, 末 sounds wrong and あと後で or てから is the word: ×顔を洗った末に、朝ご飯を食べた.
末 belongs to writing, news and formal speech. In conversation the same story is usually told with いろいろかんがえて考えて、けっきょく結局きごう〜.