"Timesharing" is how we now talk about what used to be called "custody" in Florida. Over a decade ago, Florida lawmakers realized that they needed to modernize how we talked about familial issues in the context of divorce. Too often, we found that people were arguing over labels, instead of the actual issues.
As lawmakers struggled over how to equalize not just the terminology, but the importance of both parents' in children's lives in divorcing situations, they started describing the time that would be allocated to each parent as the time that the parent would "share" with the child. This, after all, is what the parents were doing; they were "sharing" their children with one another. Once the conversation was re-framed that way, it was an easy leap to the more fluent "timesharing" term we now know and use so easily today. The term set a more cooperative tone, and removed the perceived power that came along with being designated as the "custodial" or "primary" parent, while also removing the stigma of being called the "non-custodial" or "secondary" parent.
Parents are now awarded specific days with their children each week or month. This timesharing schedule is written out in a "Parenting Plan", together with other parental rights, duties, and responsibilities. Parents can agree on a timesharing schedule and parenting plan, but the Court must consider whether an agreement is in the children's best interest, before approving the agreements.
Often times, one parent still has the children more days (overnights, to be more specific) than the other parent in a timesharing schedule, so they are the "majority timeshare parent", but that designation doesn't flow as easily off the tongue as the "custodial" or "primary" parent, so is not used as often as the other terms were. "Majority" is also not as powerful a word as "custodial" or "primary" so it helps to equalize the parents' perceived power.
Most counties in Florida have adopted standard or recommended timesharing schedules for certain situations. If you have questions about what may be customary in your jurisdiction, be sure to contact an attorney who does family law in that area.