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A picket line is a horizontal rope, along which horses are tied at intervals. The rope can be on the ground, at chest height (above the knees, below the neck), or overhead. The overhead form usually is called a high line.
A variant of a high line, used to tie a single horse, is a horizontal pole attached high on the side of a horse trailer. The attachment is designed so that the pole can be removed or folded against the trailer when not in use.