What is the Jesus Prayer Rosary?

It isn't a "rosary," though they share the same root prayer form mentioned by the desert fathers as an apostolic prayer form. The item you are looking for is a tchotki. It is used by Eastern rite Catholics and Orthodox. The prayer should be said under the supervision of a spiritual leader. It is an "aspiration" prayer, like the weird chanting prayers of the Tibetan monks, but without the chant. It is unbounded in that there are no set number of prayers. You pray until it is time to not pray. The only prayer is "Lord Jesus Christ, Son of God, have mercy on me a sinner." You breath in while saying "Lord Jesus Christ, Son of God," and breath out when you say "have mercy on me a sinner." You do not stop to take breaths because you are breathing while praying permitting you to literally take Paul's command to pray unceasingly to heart since you do not breath in between sentences. There are no meditations, just the words. Like the rosary, there are knots on a rope, but unlike the rosary, it is not a counting device. You do not do one loop, or five loops. You may do seven knots or three thousand knots. You pray until it is not time to pray.