A collection of trees is called a forest, unsurprisingly. Your graphs are considered trees only if the edges are undirected, i.e. the relationships described are "two-way", e.g. X is related to Y can be restated validly as Y is related to X. This is known as a symmetric binary relationship. If your edges are directed, then the graphs are not correctly called trees. The relationships described above are asymmetric, creating links which are also not symmetric.
You might consider searching for "forest mathematics" on wikipedia and in mathematical journals to get some other terms to consider for evaluating and describing your collection of graphs.