The growth of ice stalagmites obtained by the solidification of impacting droplets on a cooled substrate ($-50{}^{\circ }\mathrm{C}$ to $-140{}^{\circ }\mathrm{C}$) is investigated experimentally. It is shown that for any combination of substrate temperature and drop flow rate, there is a critical height above which unfrozen water accumulates at the stalagmite's tip, drips, and develops into fingers that give a star shape to the stalagmite. Both the vertical growth and the radial growth of the stalagmite are discussed through the Stefan problem and mass scaling arguments, respectively. Finally, a phase diagram that presents the stalagmite aspect ratio in function of the main control parameters is proposed.

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• Capillary interactions
• Multiphase flows