The tow company will (per state law) file for abandoned title and take ownership of any vehicles left unclaimed at the tow yard (after the 30-day hold has expired, when applicable), and you could be charged an abandoned vehicle fee.
If you will be delayed in recovering the vehicle and wish to request more time, contact the Motor Vehicle Department Abandoned Vehicles Unit at 602-712-8406.
The city has contracted with All City Towing for towing and impound services:
All City Towing
922 E. Gilbert Drive
Tempe, AZ 85281