WordNet sense 1 (any of the minute blood vessels connecting arterioles with venules):

capillary vessel

WordNet sense 2 (a tube of small internal diameter; holds liquid by capillary action):

capillary tube, capillary tubing

WordNet sense 3 (long and slender with a very small internal diameter):

hairlike

WordNet sense 4 (of relatively small extent from one surface to the opposite or in cross section):

thin