There is no universal rule that applies to every facility. Each institution sets its own property limits, and those limits can vary significantly between a county jail, a state prison, and a federal facility.
The general principle in most facilities is that books sent in from approved vendors belong to the inmate and can be kept in their cell. The practical limit is space. When books accumulate to the point where they are considered a fire hazard or a storage problem, staff may ask the inmate to donate the excess to the prison library. That is not a punishment, it is a property management issue, and most inmates would rather keep their books accessible to the general population than have them confiscated outright.
There is no time limit on reading. Inmates can read during any unstructured time in their day, which depending on the facility and the inmate's program schedule can be quite substantial. Reading is one of the few activities that is universally tolerated and encouraged across all facility types.
As for knowing whether your family member needs more books, the simplest approach is to ask them directly during a call or through a letter. If they are working through books quickly, keeping a steady supply coming is one of the most useful things a family member can do. It keeps the mind engaged and the time moving.
For ADX specifically, InmateAid has the Admissions and Orientation Handbook available on the information page of the site. It covers property rules, commissary, visitation, and other facility-specific details that are worth reading if your family member is housed there.
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