That depends on your radix. The maximum number of children of a node is the number of possible unique values of the chosen discriminator; if you use a character for the discriminator, then the maximum number of children will be the number of valid characters.
You can implement this data-structure with a radix of two, by discriminating on each bit; in this case, your trees will be deeper but each non-leaf node will have exactly two children, which might simplify the implementation.