Land inheritance is among the more complicated elements of Roman law, and succession laws changed wildly over several centuries. In almost all cases a property holder "without an heir" would have passed on his property through his will. In point of fact, succession by will and testament was in virtually all known cases the way by which inheritance was decided, even when there were known legitimate progeny, biological or adopted. When there was no legitimate biological progeny, typical practice was to adopt and to include the adopted (as with biological offspring) in the will. In rare cases we see consternation regarding biological offspring, though simple adoption was quite common in childless lines. So in his old age Hortensius asked Cato to divorce his daughter Porcia from her then-husband Bibulus and marry her to him, so that she would produce a child for him, at which point he would return her to Bibulus. According to Plutarch, Cato refused on the grounds that Porcia was already another man's wife, but for some reason considered that same logic not to apply when Hortensius asked for Cato's own wife, Marcia, who was still of childbearing age. Hortensius married Marcia for a brief time, and when she had produced an heir he returned her to marry Cato again.

Hortensius is a highly unusual case, however, and Plut., Cat. Min., 25 demonstrates ably how oddly it was thought of by Roman contemporaries--Plutarch, Cat. Min., 52 purports to translate a passage from Caesar's Anticatones that accuse Cato of using Marcia as a means of enriching himself through her. In the somewhat unlikely event that a property holder died intestate, property devolved to the offspring (including adopted children), who became sui iuris upon the death of their father, and if those were absent upon the closest agnatic line. Strictly speaking by the Twelve Tables an intestate's offspring became truly heirs--heredes--whereas if the property passed to agnatic relatives they acquired the property and only succeeded the household by usucapio, a complex type of ownership through use that was defined by the Twelve Tables and in the Principate redefined and reformed. Initially it appears that women in the agnatic line also succeeded, either by testament or by laws of succession. We know that the Lex Voconia in 169 limited the right of property holders to devolve property on women by will, and women lost the right to inherit along the agnatic line from an intestate past the third degree. If there were no agnatic proximi or they all disclaimed, the property of an intestate devolved on further relatives, expanding out into the gens. Freedmen in the Republic, who not infrequently seem to have died intestate, bypassed their agnatic relatives if they had no offspring of their own, and in that case their property devolved on their patron and his agnatic relatives. By the first century a praetorian action resolved to offer an alternative to the civil law's treatment of intestates--by the civil law, emancipated children and other direct relatives outside the agnatic line were not legally heirs, though they had as much right as offspring still within the intestate's power. The praetor's decision is complicated and later than what you're asking, but as part of possessio bonorum the late Republican praetor could call up possible heirs in sequence and have them defend their right to the property, allowing, for example, for cognate relatives to lay claims on the property, and for children regardless of their legal emancipation to inherit. Further legislation in the Principate refined the inheritance laws.

Since land ownership was a big controversy at this time due to the Gracchi brothers, would the policy on who seizes the land next matter if I died before or after their tribunal?

The Gracchi have nothing to do with any of this. It has been well established that the Gracchan land commission privatized public land, rather than confiscating private land. If possessors of ager publicus had any sort of legal right to the land at all, it would have been through usufruct and therefore not a legal ownership that could be inherited.