If no parent is specified to receive the deductions, then it's more a matter of interpretation and eligibility. Often the custodial parent will claim the deductions by default, but eligibility may also depend in part on where and with whom the child resides. The parent who has the most residential time with the child is often considered to be the 'eligible' parent, but this isn't a hard and fast rule.
If the custodial parent is not working and the non-custodial parent is, the non-custodial parent may be able to claim tax benefits that might ordinarily go to the custodial parent.
The following articles have more specific information on non-custodial tax deductions: