The sole proprietorship Josef Zdenko Dworak was founded in 1919 by Josef Zdenko Dworak, who renamed it that year to J. Z. Dworak junior, so as to avoid confusion with his father's transportation company, which was now called W. Dworak senior. Its offices were at Burggasse 52 in Vienna's 7th district, and later at Burggasse 48, while the depot and garage were at Gentzgasse 162 in the 18th district, where Dworak lived. The furniture storage and transportation activities were enlarged in 1932 to include horse-drawn carriages. After the death of the sole proprietor Josef Zdenko Dworak in 1967, his second wife Josefa continued to manage the company, now called J. Z. Dworak. It was incorporated in 1986 into the newly founded J. Z. Dworak Gesellschaft m.b.H.
Like a number of other transportation companies, that of Josef Zdenko Dworak, who was a member of the NSDAP, crops up in provenance research into state-owned objects. The works from the estate of Lothar Egger-Möllwald, who died in Italian exile in 1941, that the Gestapo had not removed, were stored with Spedition Dworak and used after the war by the US authorities to furnish villas in Vienna. A painting by Albin Egger-Lienz from this estate was restituted by the Finanzlandesdirektion in accordance with an Advisory Board decision in 2007. Moriz Grünebaum's art collection was also stored in 1941 with Spedition Dworak shortly after Grünebaum had been forced to move in with his sister. The Vienna Restitution Commission adjudged that the objects, most of which resurfaced in Auktionshaus S. Kende after the war, should be restituted.