Grandparentage testing can be used to establish the paternity of a child when samples can be obtained from the child and from both paternal grandparents (alternatively, should you wish to identify a maternal relationship then both maternal grandparents will be required to provide samples). If however the child, the mother and only one of the paternal grandparents are available, the test will be able to provide a strong indication of whether the child is related to the paternal grandparent (and therefore to the missing father), but it cannot provide a conclusive result.
It is possible to just compare the DNA profile of a child and an alleged grandparent (although we prefer that the mother is tested). This can provide an indication of a relationship but, because of the patterns of DNA inheritance, it will not always reveal the true nature of the relationship. Such an analysis will report the most likely relationship given the DNA evidence.