What is the ruling about reading Quran eg like completing one whole quran not by one person but sharing Juzz among family members or friends.
The katmah as a completation of reading the Qur'an
First how you read the quran or complete it is basically irrelevant. But if you want to complete it then each of you should have read the whole quran -no matter if it was in the correct order or not- , else you won't get the rewards of completing it (see the fatwa islamqa #50781).
The only rewards you may gain are those of what you have actually read or recited. I know the practice of distributing parts of the quran (a couple of ahzaab, aj-za' etc.) between many readers, but even if it is technically a khatmah (a complete reading) or might be more than one, as long as these readers don't listen while only one of them is reading it can hardly be considered as a khatmah for any of them.
However you might also get the rewards by reading and listening if each time one of you read a part of the Qur'an while the others where listening until you completed it.
Conclusion: one khatmah الختمة (a complete reading of the quran ختم القرآن from al-Fatiha -1st surah- until an-Nass -114th and last surah) only counts if you have read it yourself or at least listened to it.
The khatmah as the gathering when the Qur'an will be completed
However a person whom have recited the whole has a special supplication therefore it is highly recommended to invite and gather people to assist a khatma and say ameen during the supplication.
Here some references with my own tranlsation -with the exception of the hadith from islamqa- take it with the necessary care:
ان أنس إذا ختم القرآن جمع ولده وأهل بيته فدعا بهم
Anas (ibn Malik) when he was about to complete the quran used to gather his children adn wives and did supplication (ad-Darimi)
اقرؤوا القرآن وسلوا الله به، قبل أن يأتي قوم يقرؤون القرآن فيسألون به الناس
read (recite) the quran and ask Allah by it (do supplication) before people will come whom will read the quran and ask other people by it (Ahmad and at-Tabarni in his al-Kabir source for this in the former hadith)
Anas ibn Maalik (may Allaah have mercy on him) had completed a reading of the Qur’aan, he would gather his family and make du’aa’ (islamqa #65581)
مَنْ قَرَأَ الْقُرْآنَ ثُمَّ دَعَا ، أَمَّنَ عَلَى دُعَائِهِ أَرْبَعَةُ آلَافِ مَلَكٍ
The person whom completed the quran and then makes a supplication, four thousand angels will say ameen to his supplication. (sunan ad-Darimi)
Laymen would also call this khatma, but this only the session of completing the quran not what we call a khatma.