diff --git a/datatree/tests/test_tree_broadcasting.py b/datatree/tests/test_tree_broadcasting.py
new file mode 100644
index 00000000..696395ef
--- /dev/null
+++ b/datatree/tests/test_tree_broadcasting.py
@@ -0,0 +1,44 @@
+import numpy as np
+import pytest
+import xarray as xr
+
+import datatree.testing as dtt
+from datatree.datatree import DataTree
+
+empty = xr.Dataset()
+
+def int_ds(value):
+    return xr.Dataset({'data':xr.DataArray(value)})
+
+class TestTreeBroadcasting:
+
+    def test_single_root(self):
+        dt1 = DataTree.from_dict(d={'root': int_ds(3)})
+        dt2 = DataTree.from_dict(d={"root/a": int_ds(2) , "root/b": int_ds(5)})
+        expected = DataTree.from_dict(d={'root/a': int_ds(3*2), 'root/b': int_ds(3*5)})
+        dtt.assert_equal(dt1*dt2, expected)
+
+    def test_hollow_level_2(self):
+        dt1 = DataTree.from_dict(d={'root/a': int_ds(5), 'root/b': int_ds(4)})
+        dt2 = DataTree.from_dict(d={'root/a': int_ds(3), 'root/b/c': int_ds(2), 'root/b/d': int_ds(7)})
+        expected = DataTree.from_dict(d={'root/a': int_ds(3*5), 'root/b/c':int_ds(2*4), 'root/b/d': int_ds(7*4)})
+        dtt.assert_equal(dt1*dt2, expected)
+
+    def test_dense_level_2(self):
+        dt1 = DataTree.from_dict(d={'root/a': int_ds(5), 'root/b': int_ds(4)})
+        dt2 = DataTree.from_dict(d={'root/a': int_ds(3), 'root/b': int_ds(9), 'root/b/c': int_ds(2), 'root/b/d': int_ds(7)})
+        expected = DataTree.from_dict(d={'root/a': int_ds(3*5), 'root/b':int_ds(9*4)})
+        with pytest.raises(ValueError, match='not implemented for non-hollow trees')
+        dtt.assert_equal(dt1*dt2, expected)
+
+    def test_hollow_twoway_level_2(self):
+        dt1 = DataTree.from_dict(d={'root/a/e': int_ds(5), 'root/a/f': int_ds(20), 'root/b': int_ds(4)})
+        dt2 = DataTree.from_dict(d={'root/a': int_ds(3), 'root/b/c': int_ds(2), 'root/b/d': int_ds(7)})
+        expected = DataTree.from_dict(d={
+            'root/a/e': int_ds(3*5),
+            'root/a/f': int_ds(3*20),
+            'root/b/c': int_ds(4*2),
+            'root/b/d': int_ds(4*7)
+            }
+            )
+        dtt.assert_equal(dt1*dt2, expected)