Minecraft wiki entry for Development_versions, associated text: If a stalactite is hanging from a dripstone block with a water source above, it will slowly grow both the stalactite from above and a stalagmite from below.
Growth speed is random but very slow; a single growth step can take several in-game days.
A stalactite will only grow up to 7 blocks long.
A stalactite will only cause stalagmite growth if the floor or stalagmite below is within 10 blocks.
If the stalactite tip is inside water it won’t drip, and therefore will not trigger any growth.
If the stalagmite tip is inside water or there is a fluid between the two dripstone blocks, it will not receive the water drops, and therefore will not be grown by a dripping stalactite.
A stalagmite or stalactite will never grow when submerged in fluid.