When it comes to conflicts, there are many synonyms that can be used instead of "fights over." Some alternatives include "arguments about," "disputes regarding," "contests for," "battles over," "struggles to secure," "clashes for control," "quarrels over," "contentions for," "encounters regarding," and "controversies surrounding." Each of these phrases can convey a slightly different nuance, such as the intensity of the conflict or the specific object of contention. However, all of them capture the idea of a struggle or competition for something, whether it be power, resources, recognition, or some other goal.