It has been narrated that these gardens (hawa'iṭ) were endowments (waqf), and the Messenger of Allah سبحانه وتعالى, peace and blessings be upon him and his family, used to take from their yield to spend on His صلى الله عليه وعلى آله وسلم guests and those who passed by Him صلى الله عليه وعلى آله وسلم. After His صلى الله عليه وعلى آله وسلم passing, Al-Abbas came to dispute with Sayyidah Fatimah صلى الله عليه وعلى آله وسلم, peace be upon her, over them (gardens). Imam Ali ibn Abi Talib عليه السلام, peace be upon him, and others testified that they were endowments specifically designated for her (Sayyidah Fatimah صلى الله عليه وعلى آله وسلم). Among the well-known names of these gardens is Al-Mithab, though I have also heard Sayyid Abu Abdullah Muhammad ibn Al-Hasan Al-Musawi - may Allah سبحانه وتعالى grant him continued success - mention that it is known among them as Al-Mitham.
Commentary #2