Did the companions (sahaba) write down hadith?

Dr. Muhammed Mustafa Al Azhami's Phd thesis at the University of Cambridge answers this well.  Hadith literature among 50 Companions:  1.  Abu Ayyub al Ansari had some Hadith written and sent to his nephew. His great grand son have Hadith collection written from him which consists of 112 ahadith.  2. Abu Bakr as Siddiq lettered the ahadtih concerning zakat to Anas bin Malik and a letter to Abdulla ibn Amr ibn al Aas containing some ahadith.  3. Abu Bakrah ar Rhaqafi wrote a letter to his son the Governor of Sijistan on Hadith about Business of justice.  4. Abu Huraira transmitted 1597 unique ahadith. * Hasan ibn Amr ad Damari saw many ahadith books with him. * Abdul Aziz ibn Marwan had written down almost all ahadith of Abu Huraira. * Al A'mash has 1000 ahadtih of Abu Huraira written via Abu Salih who had written from Abu Huraira. * Bashir ibn Nahik wrote ahadtih from Abu Huraira and presented them to him and obtained permission to transmit. * The Sahifa of Hammam ibn Munabih from Abu Huraira which is still extant in Musnad Ahmad contains 136 Ahadith. * Marwan bin Hakam made a collection from him. * Muhammad ibn Sirin had a book from him. * Said al Maqburi had a book from him.  5. Abu Musa al Ashari was against writing ahadith and also erased the writings of of his students, but he sent some ahadith in writing  to ibn Abbas.  6. Abu Rafi used to be visited occasionally by ibn Abbas for Prophet's deeds and saying and have written down. He once gave a booklet on the Salah and Dua to one of his students.  7. Abu Sa'id al Khudri transcribed ahadith even though the Hadith against ahadith is attributed to have come via him.  8. Abu Shah al Yamani was the one who had the khutba written for by the Prophet (saw)  9. Abu Umamah  10. Abdullah ibn Abbas had often consulted and written down ahadith from multiple senior companions. At least 9 students wrote ahadith from him.  11. Abdullah ibn Abi Awfa  12. Abdullah ibn Amr ibn al Aas' Sahifa Sadiqa is a well known books of Hadith of the era. He was very keen and proactive on recording ahadith whenever an opportunity arose. The Sahifa Sadiqa reportedly contained nearly a thousand Ahadith. He also recorded the Prophetic biography, the accounts of Prophetic battles and legal verdicts of Umar ibn al Khattab. Due to him being very proactive in recording some of his companions advised him not to record the words of the Prophet (saw) at seemingly inappropriate situations such as when he's angry etc. However he had received the approval of the Prophet (saw) to record any and all statements of the Prophet (saw). He has several students. At least 7 of his students wrote ahadith from him.  13. Abdullah ibn Mas'ud was known for disapproving the writing of ahadith yet he had book which was made known by his son who swore that it belonged to his father.  14. A. ibn Umar was known strict word for word transmission of ahadtih with zero toleration any variance from the original statement of the Prophet (saw) regardless of the insignificance of the impact on the meanings. He had a book from Umar and written down a lot of ahadith.  15. A. ibn az Zubair wrote a letter to Abdullah Ibn Utbah on some legal issues by quoting some ahadtih.  16. Aisha, Umm al Mumineen, transmitted a lot of ahadith and had some of them written. * Muawiyah and Urwah Ibn az Zubair wrote ahadtih from her. * At least 3 people wrote ahadith from her.  17. Ali ibn Abi Talib had written on a large parchment from what the Prophet (saw) had dictated to him (saw). He also had a Sahifa from the Prophet (saw) and a Kitab of the Prophet (saw) on Zakat and Taxation. At least 8 students of his wrote ahadith from him.  18. Amr ibn Hazm, the Governor of Najran appointed by the Prophet (saw) had letters from him on the rituals and other matters such as taxation, spoils of war, diyat etc.  19. Anas bin Malik valued only those narrators who wrote down ahadith hence he wrote a lot of ahadith and had all his students write them down. At least 16 people wrote ahadith from him.  20. Ansari. An anonymous Ansari who is said to have written down what the Prophet (saw) said.  21. Asma bint Umais  22. Al Bara ibn al Azib had students who would write down ahadith.  23. Ad Dahhak ibn Sufyan al Kalbi wrote letter to Umar against his views concerning inheritance by quoting the Prophet (saw).  24. Ad Dahhak ibn Qais ibn Khalid wrote letter to his student containing ahadith and those ahadtih have reached us via Musnad Ahmad.  25. Fatima (ra) wrote ahadith from her father.  26. Fatima bint Qais wrote a letter to Usama bin Zaid, her husband, regarding the condition of the Prophet (saw).  27. Hasan, the leader of youth in paradise, had a book and encouraged his sons and nephews to write down ahadith.  28. Itban ibn Malik was found so impressive by Anas bin Malik that he had his son write down ahadith from him.  29. Jabir ibn Abdillah compiled a booklet on Hajj and Umra. At least 14 students of his wrote ahadith from him.  30. Jabir ibn Samura wrote ahadith to Amir ibn Sa'd.  31. Jabir ibn Abdillah al-Bajali wrote ahadith in a letter and sent to Muawiyah.  32. Muadh ibn Jabal had a book concerning sadaqat and other books on ahadith.  33. Muawiya ibn Abi Sufyan used to teach ahadith and had order other companions e.g. * Aisha, Mughira et. al. to write down ahadith.  34. Mughirah ibn Shu'bah wrote at the orders of Muawiya.  35. Muhammad ibn Maslama al Ansari had a booklet found of his after his death.  36. Nu'man ibn Basheer had some ahadith written to his son and his students.  37. Rafi ibn Khadij had some ahadith written regarding the sanctuary of Madina.  38. Sa'd ibn Ubadah had collected some ahadith in a book.  39. Sahl ibn Sa'd as Sadi wrote ahadith.  40. Salman al-farasi had some ahadith written to Abu al-Darda.  41. Samurah bin Jundub had written ahadith and transmitted it to the likes of Hasan al Basri, Muhammad ibn Sirin, and lengthy book to his son Sulaiman which is partially preserved in Mu'jam al Kabir of Tabarani.  42. Subai'ah al Aslamiya wrote some ahadith regarding iddat to someone who had requested her.  43. Shaddad bin Aus ath Thabit, nephew if Hassan ibn Thabit, dictated ahadith to his companions on way to Hajj.  44. Shamghun al Azdi al Ansari was the first one to write ahadith on both sides of papyrus which he pressed and sew together.  45. Ubai ibn Ka'b had a lengthy Tafsir which was transmitted to his student. Also he had written a letter to two people who had a conflict regarding the Prophet's (saw) method of prayer.  46. Umar ibn al Khattab, Amir al-Mumineen. It is said that initially he wanted to compile all the ahadith under the patronage of the government and received unanimous support from the Companions. However he reconsidered the decision and then aborted the initiative and ordered all the people who had written down the ahadith to burn their parchments. This narration is mursal. * It is reported that he detained Ibn Masud, Abu Dhar and Abu al-Darda due to the volume of their ahadith transmission. * He used to quote the Prophet (saw) in his letters. He also had compiled some documents from the Prophet (saw) concerning financial and taxation matters.  47. Usaid ibn Hudair sent some ahadith on legal matters to Marwan.  48. Wathila ibn al-Asqua dictated ahadith to his students.  49. Zaid ibn Arqam wrote ahadith to Anas bin Malik.  50. Zaid bin Thabit compiled the first book on Fara'id which was transmitted by his son Kharija, one of the seven fuqaha of Madina and Qabisa. The introductory pages of this book are still preserved in the Mu'jam of Tabarani