UTMA account in Illinois. I want to remove my child (no longer a minor) from this account (with his permission). Is this a taxable event?

Are you simply wanting to remove your name as custodian, or are you taking ownership of your child's assets?

I set these UTMA accounts up to help fund the kid's educations.  The kids understand that while they have legal rights to access this money (they are no longer minors), it's not their money.  They will release ownership willingly.  I want to remove them as owners so that they will no longer be responsible for any dividends and capital gains on their tax returns.  Thanks for your thoughts on this.

It's just the opposite. It is their money.

The actual mechanics of affecting the change you desire is not clear to me.  That's more of a legal question, not an income tax question.  

I'd expect that you would have to take your name off the accounts as custodian or transfer the assets out of the account to new accounts in the children's names.  (That's the "mechanics.")  The children would then gift the assets back to you; generally that would entail a closing out of their accounts and transfers in kind into your account.  There could be gift tax issues, depending on the amounts involved and whether you're married or not.  I guess as long as they understand their rights there's no problem.

When handled properly it is not a taxable event. Talk  to the firm where the account is kept on how to do it. You'll first have to  re-register the account in his name. Then he will transfer shares of the stocks and mutual funds to a new account in your name. Your son's cost basis in the shares transferred become your cost basis.

You'll probably have some paper work, as it is not usually done this way. The funds are legally his. Your son may be required to file a gift tax return, as he will be making a gift of his shares to you.

 "Gift Tax" is somewhat of a misnomer.  Even though a gift tax return may be required, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/INF12127.html