Here is the solution to this problem, which works correctly (credit to Steve Kass: http://stackoverflow.com/users/139164/steve-kass):

WITH cte(CarID,hier) AS (

SELECT CarID, CAST('/'+LTRIM(CarID)+'/' AS varchar(max))

FROM Car

WHERE CarName = @StartCar

UNION ALL

SELECT c2.CarID, hier+LTRIM(c2.CarID)+'/'

FROM Car AS c

JOIN cte ON cte.CarID = c.CarID

JOIN CarPart AS c1 ON c.CarID = c1.CarID

JOIN CarPart AS c2 ON c2.PartName = c1.PartName

WHERE hier NOT LIKE '%/'+LTRIM(c2.CarID)+'/%'

)

SELECT

c.CarName, cp.PartName

FROM Car AS c

JOIN CarPart AS cp ON cp.CarID = c.CarID

JOIN cte on cte.CarID = c.CarID