We took custody of our grand-daughter December 1, 2016. Do we say that we ahve a dependent? If so, how will that affect my daughter's taxes for the rest of the year?

Was your daughter a single parent the rest of the year?

You say "we took custody."  Presumably you refer to your spouse and yourself.  You wouldn't be able to claim your grand daughter as an eligible dependant.  If your daughter was a single parent while she had custody she is able to claim the eligible dependant credit.

However as you now have custody of your grand daughter you will want to inform CRA of this with the RC66 form so that you may receive the Canada Child Benefit.

Since UCCB is replaced by Canada Child Benefit, you would not receive this benefit, or the RC62 slip.

Tony that has nothing to do with the question.

I'm commenting on your response, which is to the question.

Not necessary Tony.

And not relevant.