As is probably mentioned below, OLIVER! was revived on Broadway in 1983 with Ron Moody recreating his original and movie portrayal of Fagin, and Patti Lupone as Nancy. It was basically an exact replica of the show that opened on Broadway back in the 60s with the same director (was it Peter Coe?), and the same revolutionary (in the 60s) set design by Sean Kenney. It closed very quickly after a pan by Frank Rich (among others).
Back in the late 90s Cameron Mackintosh (sp?) wanted to bring his new OLIVER! to Broadway. It had been a big hit in the West End (with Jonathan Pryce as Fagin, followed by variety of other stars like Jim Dale) and Mackintosh was anxious to open it on Broadway. However, AEA insisted that all the children in the production (in London there were about 40 and I think they were double cast) be paid regular Equity Broadway pay, even though most of them would leave after the first two number (Food Glorious Food, and Oliver!). So, they were to get full pay and benefits of a Broadway show contract even though they were free to leave after the first 10 minutes of the show. Mackintosh balked at that and tried to work out a deal, but AEA would not budge, and that is why the Mackintosh OLIVER! revisal never opened on Broadway. But, Mackintosh did bring a non-equity tour of the show to the US right around 2000 or 2001 and was able to use a large cast of children.
I believe Mackintosh is in charge of any big new revivals and he would want to exert a lot of control over the proceedings. But the show is done regionally around the country.