Unless they've changed the form recently, there should still be questions about children, and you should still have to provide their passport, birth certificate and letter confirming their address.
They introduced this requirement for ILR a year or two before it was introduced for FLR(M), and as far as I am aware, it is still a requirement to provide information about your non-applying children.
They ask for details of children, because if the application falls for refusal (whether it be FLR or ILR), they will look to see if you can be put on the 10-year path under Article 8... and the main thing they look at for eligibility is whether you have any UK citizen children living in the UK whose lives would be seriously negatively affected if your visa were to be refused.