It is $13k for each contributor. For example, you open ONE account for your kid, anyone can contribute up to $13k each year to this account. If the kid doesn't have grand parents/uncles/aunties who can contribute, the parents can contribute up to $26k/year/ The beneficiary can be changed - That is if the older kid can use them all, you can use it for younger kid/niece/nephew.....even yourself if you plan to go to univ when retire.
Most of time the plan may have limitation on fund choices (very alike 401k although the fund management expenses could be higher)