Piano Concerto Candenzas

I've begin to prepare for a piano concerto contest and have some questions about cadenzas.

I know lots of composers write out the cadenza, or do so later. Are there any concertos were performers improvise a cadenza? If so, does any one have any videos to recommend?

If a composer writes a cadenza for their concerto, is the performer expected to use that one? What if the composer writes it after publishing the concerto.

Are there many different published cadenzas for most concertos, or just one?

Thanks.

This is a difficult question.

In the Classical period (including Beethoven for now) the cadenzas were improvised by the performer on themes used in the concerto. However, people like Clara Schumann and other great pianists wrote cadenzas for other people's concerti. So you have just as much of a right to write your own cadenza.

Bach. (No cadenzas)

If this is for a competition then go by the widely accepted one, but if it is just for performsnce, then experiment a little!

if you are going to improvise, please please please do it in style. these things are focused on structure!! there are great cadenzas, listen to a few performances of the concerto and see what different cadenzas performers use. if in the end, make sure it works to your own technical strengths since that is the point of the cadenza! but for goodness sake don't put a prokofiev-esque cadenza in a mozart concerto!