UML threads

I am having trouble working out how to model this situation correctly in UML.

Thread 1 and 2 are running concurrently

… |—>thread1
… |—>thread 2

Thread 1 is running, but when an event occurs, thread 1 creates a new thread, thread 3… however thread 1 continues running.

All of the examples I have seen show a split followed by a join - is it ok to show thread 1 splitting to create thread 3 and going back to itself? As this means there is no need for a join?

thread 1 ---->|------->thread 3

Sorry not a very good diagram, but thanks If you can understand this!

Have a look at sequence diagrams, they will do that for ya or statemachine diagrams.

Sequence diagrams show the interaction and time order of a message.
Statemachine diagram, shows event-ordered behaviour of an object.