There was no agreement for a long time regarding the place of the stole in the sequence of the pontifical vestments. Here bishops wore it above the dalmatic, there between dalmatic and tunicle, elsewhere beneath theb tunicle above the alb. Only the end of the first millennium brought a uniform practice according to which was since worn generally above the alb by bishops. The deacons wore the orarium under the dalmatic according to the Roman Rite, in contrast over the tunic of their office, the so-called alba, according to the Gallican and Hispanic Rite. In the 12th century we find the orarium still worn over the dalmatic only in the Ambrosian Rite and in Southern Italy. Here, where the custom certainly owed its origin to an influence of the Greek manner of wearing the diaconal orarium, the Roman practice was adopted in the 13th century, whereas in Milan the deacons still wear the stole over the dalmatic today. That the deacons put on the stole in the form of a sash only developed later. In the beginnign of the 12th century it was already custom, not, however, already in the 9th century. At that time rather the deacon only on penitential days, on which he would wear the the planeta in the manner of a sash from the Gospel onwards, wound the stole around in the form of a sash, together with the planeta. From this exception then gradually developed the later rule.
The picture accompanying this post shows St Lawrence wearing the stole over the dalmatic in Halberstadt Cathedral.