Documents establishing the relationship to the principal — marriage and birth records — and their own identity documents. TD dependants may study but are not authorized to work.
Relationship documents, and a clear rule on work
Hypothetical example: The dependants' file is smaller than the principal's but it has to be exact. The relationship is proved by civil documents, so a marriage certificate and each child's birth certificate should be available in original or certified form rather than as photographs of documents kept elsewhere. Names that differ across documents, because of a change on marriage or a variation in spelling, should be reconciled with the record that explains the difference.
The rule on activity is straightforward and should be settled before departure: a TD spouse may live in the United States and may enrol in study, but may not accept employment, and children in TD status may attend school but may not work. A spouse intending to work needs an independent basis assessed on their own facts, which is a separate matter with its own evidence and its own timeline.