In most cases a smoking wick is a sign that the wick chosen for the candle was too large. When a wick is too large, it will try to consume more melted wax then the flame can efficiently burn. The unburned material escapes the flame as soot or smoke. If there is more fuel flowing up the wick than can be fully combusted with the available oxygen, smoke is generated which is the visible remnant of the unburned fuel. There are many reasons for carbon head mushrooming on wicks.
Cored wicks are usually the most prone to carbon formation.
By their design, cored wicks are made to be rigid. Because of the tight braid, cored wicks are more prone to becoming clogged with things from the wax formulation. Cored wicks also tend to burn in a cooler area of the candle flame, so the impurities that have built up can not be combusted in this part of the flame. As a result a carbon head forms. The best cure for this problem is testing of the wax formulation and wick combination.