What happened to kiev when yaroslav the wise died in 1054 ce?

when yaroslav the wise died in 1054 ce city of Kiev remained major city of Rus and one of the biggest cities in Europe but Rus itslef entered into period of natural feudal defragmantation but it must be stated that there was no legal granted lineage and any duke or prince of russian (or rather ruthenian) prrincipalites could lay his claim to the Kiev