My friend who is a nanny says the free range method is what she's always used, and in her experience it works best. She said the thing is, "they want to put it somewhere." So when there's no diaper to put it in, they'll go for the toilet.
Personally, I was never in ny big rush and Dagmar wasn't ready for a long time. She just wouldn't go with enough consistency to justify taking the diapers away, so she was still in diapers until June-when she was almost 4-and one day she just started using the potty, and only very rarely had an accident after that. At least with pee. Poo took a lot longer-as in, it's only in the last few months that we don't have pooey accidents anymore.