In May 2018, news came from Bloomberg that the UAE were going to ease the rules on foreign ownership (https://www.bloomberg.com/news/articles/2018-05-20/abu-dhabi-mulls-change-to-expat-residency-to-spur-investments)
Normally, foreigners have full ownership of their companies in free zones only.
Outside of the free zones, companies must find local partners who will hold 51% of the shares.

Where do we stand now? How is this new law being implemented?

First of all, although in force since the beginning of the year, the law is still a work in progress. However, the authorities have identified sectors that are excluded from this program. Oil, Banking, Financial and Insurance are out of scope; hence excluded from this program.

Otherwise, the process is straight forward. Along with the application form, one needs to provide a business plan with detailed projected financial forecasts and be able to implement an “emiratisation “policy in the company.
The profiles of the companies which can benefit from this new law are listed companies and companies which already have a track record and are able to implement the emiratisation policy in their organisations.

More to come on the subject as the law is at its early stage of implementation.

Sources:

https://www.arabianbusiness.com/politics-economics/410580-uae-begins-implementing-new-100-ownership-10-year-visa-for-expats

www.M-hq.com