I think you mean adverse possession. Based on your comments, it is an extremely strong case. You don't get any more open and notorious use of someone's property then making them pay to use their own property.
Law Offices of James A. Abate Jabatelaw.com (732) 412-2364
Although I am not licensed in New Jersey, there are some basic issues to be determined. First, is there a recorded easement giving your condominium the right to maintain the pool on the adjacent condominium's land? I would expect so because no construction lender would have allowed a significant known encroachment without an easement. Second, if there is no existing easement, because it is difficult for a condominium to dispose of a portion of the common elements, an easement might be easier to obtain than title to the land. Third, if there is no existing easement you may have acquired title to the encroached upon land by adverse possession. If so, a lawsuit to quiet title could resolve the issue by court order. Finally, if the adjacent condominium unit owners enjoy using your pool, refusing to allow their use of the pool until the matter is settled may get their attention. Good luck.
I'm right up the road in Sea Isle City, NJ. I specialize in condominium law, real estate, and related matters. I will down in Cape May on Tuesday 7/10/12. I can swing by to meet with you to look at condominium documents, your condominium survey, etc. Have you had a survey prepared in recent years? Do you have any type of written agreement with the other condominium? Has your condominium board entered in any type of agreement or enacted any resolutions over the past 20 years regarding this situation? If interested in a consult, please contact me at firstname.lastname@example.org.