Hi,
well I am from Dubai and the process of getting a visa is a bit different from what "australia" said. When you buy a freehold property in dubai/ajman you are entitled to a Residence visa of the UAE. The Owner of the building has no rights on granting the visa etc.. You just have to submit your papers including your property ownership documents to the UAE government for the visa. And after completing their process they will grant you your visa.

Its a fairly simple process and many many people are coming to dubai now because of the vast opportunities here in terms of job and good and safe living.

If you need any assistance in buying property in dubai, do not hesitate to contact me as we have a real estate agency and would be glad to help you out.