Malik taught in Medina for decades and did not travel except on pilgrimage, which in a discipline transmitted face to face meant that students came to him. The Muwatta was carried away in several recensions taken down by different pupils, and the differences between them are themselves evidence about how such texts were transmitted; the recension of Yahya ibn Yahya al-Laythi, an Andalusi, became the one usually printed.
A school in this sense is not an institution with a building. It is a body of doctrine, a chain of teachers, and eventually a set of books that later jurists agree to work within. The Maliki school took shape after Malik through students such as Ibn al-Qasim and Sahnun, whose Mudawwana organises Maliki positions into a working manual, and it travelled west with them into Ifriqiya, the Maghreb and al-Andalus.
His relations with power were not comfortable. The biographical tradition records that he was flogged on the order of the governor of Medina over a ruling touching an oath of allegiance to the Abbasids, and that the episode raised rather than lowered his standing. Later caliphs are said to have proposed making the Muwatta the law of the empire and to have been refused, on the ground that the regions had received different teaching and should be left with it, which if true is an early statement of legal pluralism as a principle.