In some forests there are palm trees that are not owned by anyone. Is it permissible for us to own them? If yes, there are trees that I inherited from my grandfathers which were not originally theirs. What should we do with them?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

The forest which is not owned by anyone and the trees that you preceded others in taking care of are part of your possessions. By the same token, you own what your grandfathers owned by being the first people to take it. Asmar ibn Mudharris said that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Whoever reaches a permissible thing first [apart from disused land such as game (animals or birds for hunting) or wood] then it is his.” [Abu Daawood and Al-Bayhaqi; weak chain of transmission] In another narration, “The first one to reach a thing that was not reached before him has the right to own it.” [Adh-Dhiya’ Al-Maqdisi: authentic]

The inherited trees from your fathers and grandfathers are valid estate under Sharee'ah that is permissible for you to own and to distribute according to the Sharee'ah rules of inheritance.

Allaah Knows best.