Just like in the big illusions, in which a girl is cut into three parts, asked to borrow a cigarette is cut into three pieces and VISIBLE immediately after it is healed. 

Note that the cigarette is never out of sight of the viewer, in fact this is encouraged to mark with his signature one of the three pieces of the cigarette cut, and find his signature on the cigarette healed. 
This article is provided to you with a real cigarette Marlboro.