What are the conditions for removing training wheels?
Consensus seems to be more and more this:


  Do not use training wheels.


The most important part of cycling is not the pedaling, but balancing and steering. Steering is mostly done by leaning (therefore balance) and not by turning the handle bar.
Training wheels do not help in learning to balance the bike and actively prevent leaning.

Therefore it might be better to start with a balance bike (no training wheels, no pedals) to learn the essentials and add the easy part of pedaling afterwards.