Seen as either
極（きわ）まりない or
極（きわ）まる, this grammar structure makes use of the core meaning of the う-Verb 極（きわ）まる 'to be at the extremity of (A)', and will most often be translated simply as 'extremely (A)'. In most cases, this grammar pattern will appear following words that indicate some kind of negative state or emotion.
極（きわ）まる will be used immediately following な-Adjectives, while
極（きわ）まりない will come after こと when either a な-Adejctive or い-Adjective precedes it.
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傘（かさ）をさしながら自転車（じてんしゃ）を運転（うんてん）することは危険（きけん）極（きわ）まる行動（こうどう）なので、もっと厳（きび）しく取（と）り締（し）まるべきだ。
Riding a bicycle while holding an umbrella is extremely dangerous behavior, so the police should more strictly enforce the law.
理不尽（りふじん）極（きわ）まるクレームを言（い）われるたびにノイローゼになりそうになる。
Everytime I get an extremely unreasonable complaint, I feel like I'm going to have a mental breakdown.
この会社（かいしゃ）ではFAXを使（つか）わなくてはいけないので、不便（ふべん）なこと極（きわ）まりない。
Since we have to use FAX at my company, which is extremely inconvenient.
この展望台（てんぼうだい）から見（み）る景色（けしき）は美（うつく）しいこと極（きわ）まりない。
The view from the observatory is extremely beautiful.
In the case of な-Adjectives, it is not a requirement that
極まりない be preceded by なこと, and it is actually more common for it to directly follow the な-Adjective without な.
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目上（めうえ）の人（ひと）に向（む）かってその口（くち）の聞（き）き方（かた）はなんだ。失礼（しつれい）極（きわ）まりないやつだな、お前（まえ）は。
Why are you talking in such a manner to a person that is in a higher position than you? You are an extremely rude person, aren't you?
極（きわ）まりない is not the negative form of 極（きわ）まる, but the noun 極（きわ）まり 'the extremity' followed directly by the い-Adjective ない, with が omitted between them. This means that the more literal translation for the difference between the two would be something like the following.
失礼（しつれい）極（きわ）まりない - There is no limit to the rudeness of (A).
失礼（しつれい）極（きわ）まる - The rudeness of (A) goes to the limit.
As can be seen, while the meanings are opposite in some sense, the actual nuance of (A) being 'extremely' something remains the same. The actual negative form of 極（きわ）まる would be 極（きわ）まらない, and would mean that something does 'not go to the limit of (A)'.