Waxes are primarily hydrocarbons - organic substances containing carbon and hydrogen.
When a candle wick is lit, the solid wax slowly melts and is drawn up the wick by capillary action into the flame where it vaporizes and reacts with oxygen in the air. In the combustion process the wax turns into primarily carbon dioxide and water, along with carbon monoxide, nitrogen oxides, and soot.
So all three phases of candle wax are present during burning. The solid which melts, then vaporizes as it burns.