Purely the divisions?

The Ottomans divided their territories into administrative states, called Vilayets or Wilayahs (the latter is the Arabic) which were in turn subdivided in administrative districts or Sanjaks.

Modern Iraq consists for the most part of the three Vilayets of Mosul, Baghdad and Basra, covering roughly the northern, middle, and southern third of the country, respectively. The Vilayet of Basra also included modern Kuwait and the borders were a little bit fuzzy in comparison with how things were drawn up but those three cover the vast majority of that territory.

For Syria, for much of Ottoman history the entirety of Greater Syria was administered as the Vilayet of Syria (or Damascus) but this was broken up in the 19th century to include the Vilayet of Beirut covering much of the Mediterranean cost, (edit) the Vilayet of Aleppo which includes that city as well as land to the west to the Syrian coast as well as extending north into modern Turkey, and the directly administered Sanjak of Jerusalem. These administrative divisions today include the modern Israel and the Palestinian territories, Jordan, Syria and Lebanon.

Each Vilayet was governed by a regional governor which, prior to the end of the 19th century, typically exercised a great degree of local autonomy. The Tanzimat reforms and the Ottoman constitutional period led to increased efforts at centralization and Ottomanization/Turkification, culminating in the return of constitutional rule under the Committee for Union and Progress, perhaps better known by their moniker as "the Young Turks."

During WWI Djemal Pasha was granted essentially total and control and autonomy to fight the war over the entirety of Greater Syria regardless of formal administrative divisions.

I'm afraid I'm not an Ottoman specialist so I can't speak too much to day-to-day administrative practices and normal governance but hopefully that answers your question as to the geography of administrative breaks at least.