Lymph capillaries are also known as lymphatic capillaries. They are very small vessels which have thin walls and are sealed shut on one end. They're found in the spaces between cells everywhere in the body except in non-vascular tissue such as bone and in the tissues of the central nervous system. Lymph capillaries' primary function is to drain extra fluids in the tissues from around the cell when it's ready to be filtered by the lymphatic system.