As already answered, there's no branched single strokes in Illustrator. But there's no need to make joints as you draw. A branch can well be independent object.
A random stroke with the pencil tool. Before you draw, double-click the tool icon to get the smoothing options onscreen.
Round stroke ends are selected to get some direction tolerance in the branches. A branch is at first drawn a little aside, because the Pencil easily modifies the old stroke if you start a new on it. The new one can be placed exactly with the direct selection tool. For smooth branching start the drawing nearly to the same direction as the older stroke.
Stroke ends are faded with the Width Tool.
A new branch is added. Both ends must be adjusted with the width tool.
If you later need a single solid shape for easy moving or scaling, you can group the parts. Or you can convert strokes to paths (=closed filled shapes) and join the shapes with Pathfinder panel's Unite. Save the original stroke-only version if you end to unite all. The united shape is virtually undeditable.
You must allow stroke scaling in the preferences if you want to scale the stroke-only version.