Many people think that when they say the rosary, getting to the end of it - finishing it - is the goal. But it is not. The rosary, like any other prayer, should lead us to a closer relationship with God. So when you are sitting in the Adoration Chapel, or alone (I'm not talking about the rosary said with a group of people), and saying the rosary, and a feeling of immense love comes over you, stop the rosary and just sit and soak in that love. This "hug" is a gift from God. Many call it "warm fuzzies". The mystics refer to it as "consolations." This gift is also called a blessing, or grace. It should not be the purpose of our prayer - to get a thank you from God, - our purpose is to grow closer to God - but when we do get this thank you, accept it, soak in it, let it change you, bring you happiness, joy, peace. These should be the feelings afterwards, if it is truly from God.
My spiritual director said that many people ignore these feelings because they are too anxious or in a hurry to finish the rosary to get it done, forgetting that prayer should lead us to this union with God.
Some fall asleep while in the Adoration Chapel. Sometimes this is just because we are tired, and God gives us rest, but sometimes it is a deep consolation. One tells the difference by how you wake up. If you awake feeling filled with love, as if held in the arms of your lover, then this sleep was a consolation from God.
The rosary is a prayer, honoring the Mother of God. It is asking her for her prayers for us - now and at the hour of our death. The meditations said before the Our Father - the joyful, luminous, sorrowful and glorious mysteries, help us think about the life and passion of our Lord Jesus Christ. It is a vocal prayer and meditation prayer that may lead to contemplative prayer - the deep rest, a gift from God as a thank you. This gift is also called a blessing, grace.