See, I have a different slant on it, with DC of (almost) 17 and 15. 
And slightly differing circumstances excepted, as we home own.
We have put away a small amount each month since we could afford to do so, not quite since their birth, into savings accounts in their name but with my overall control.
About 2 years ago, I changed the accounts into their own names. DS is nearly 17, so has a debit type card. DD's, you can withdraw money.There's circa £3k in each.
They get £40 pcm each put in, but no other cash whatsoever from us.
We thought long and hard about this. Theoretically, they could both go out and blow the lot. I told them this, but also that I hoped they would be sensible and realise they can spend as they see fit, but it's also a brilliant lump sum for things they may wish to do or fund as they get older. It's theirs to choose to do with what they will.
In practice, 2 things happened that I recall. DS used his card to pay for game down loads, and spend a full months money in a week, was shocked at how the £3.99 here and there added up so quickly and didn't make the same mistake again.
DD gave everyone very generous Christmas presents one year, and again, also realised that a Jack Wills top is basically one whole months money.
I think it's taught them loads about money, but also that we trust them to make sensible choices financially.
However, if they blow the lot at some point, that's their decision to make and live with. But that will make buying a car or uni life or whatever a lot tougher.
Both are far more sensible that we were at that age.
Just throwing that into the mix.