Because the concept of ownership is so important in FlowBasedProgramming, no node in the tree should have more than one parent. Thus the "root" is owned by a process, or is in transit between processes, and every node in the tree is owned by exactly one other node or by the root. This is a "? tree" - I'm sure there's a name for this kind of structure.
The concept of ownership is independent of the tree structure itself, so I don't think there's a name for this.
Actually, for immutable IPs I'm not sure why this restriction on ownership would be necessary -- in that case handles can be copied freely and it does not matter which processes hold copies.
[Ah.. on reading e.g. http://www.jpaulmorrison.com/fbp/tree.htm , it seems there is no assumption of garbage collection in the FBP model. In an implementation based on a GC'd language, it would be natural to allow arbitrary graphs of IPs.]
Trees may be converted to structures of substreams and vice versa, where grouping is marked by "signal" InformationPackets.
See also the J-D. Warnier notation, described in a number of web sites - there is an example in http://www.jpaulmorrison.com/fbp/simpapp3.htm.