Will turbo tax automatically remove children that hit the age of 19 from your return so that they can claim themselves on their own taxes?

You will go through the interview for the child and TT will determine if they still meet the dependency rules.  Most 19 year old still are dependents and if they are, they can not claim themselves and would have to answer on their own returns that they can be claimed by someone else.  The IRS has an online Whom may I claim Q&A here https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent
I hope this was helpful.

Certainly not.  One reason is that many 19 year olds still qualify as dependents.