Kalk paste.
Some folks suggest ingecting them with boiiling water, freshwater dips or lemon juice, however I find these to be less than 100% effective. Not sure if this is the only issue for tanks, usually if you have a
Aiptasia spp, you also have
Anemonea cf. majano as well (much harder to eliminate). Forget the freshwater, these are tidal animals that withstand extended periods twice a day of both air and potentially fresh water (rain). They will just make a mucus cocoon and wait out the return of SW (remember that most of these have already survived shipment on the live rock and days outside a water column). Also, they do not have to have a source of heterotrophic food items to survive and thrive; they are zooxanthellate omnitrophs, and are quite capable of surviving as a 100% autotrophic organism. The availability of both DOC's and particulate food items will just be the iceing on the cake for their sudden bloom and growth, so limiting feeding will help, but will in and of itself not stop their growth. Get some
true Peppermint shrimp (
Lysmata Wurdermanii), and not Camelback shrimps (
Rhynchocinetas durbanensis) which look quite similar in general appearance, but differ in the presence of the characteristic hump in the tail area for the Camel shriimps just past the carapice and in their coloration intensity.
Lysmata wurdermanii may not be able to take down very large specimens of
Aiptasia spp, but kalking the major ones, concurrent use of the Joe's Juice, then leaving the Pepps to do the dirty work is probably the most effective means of ridding infested rock of this pest anemone. Their forte is in taking down the small (tender) specimens of
Aiptasia. Keep the shrimps in the tank permanently, and do not feed the tank any more frequently than every 3 days while trying to rid the tank of the infestation, as feeding will reduce the desire of the shrimp to eat the anemone (they get full???

).
As far as the
Anemonea cf. majano, kalk paste seems to work the best, but I have not seen wht I would consider a really effective means of controlling them short of a regular cleanup of the little b@$t@rd$ every 3 or so months with a turkey injector (those of you that deep fry whole turkeys know what I am talking about) full of kalkpaste the consistency of toothpaste. Bury the little pests under a pile of the kalkpaste.
BTW, I would much rather use kalkpaste than lemon juice or any other organic acid in the tank, as unless the tank is quite small, the kalk will at worst form excess buffer and calcium, and if it gets too high, will precipitate out harmlessly, which is more than I can say for what the organic acids of lemon juice or vinegar injection do to a system's chemistry...
HTH