German Corps had one or several "Arko" (Artillerie-Kommandeur), staffs to lead attached army artillery. They didn't have own troops, they led battalions attached to "Artillerie-Regiments-Stab", see below. They also typically had a "Korps-Nachrichten-Abteilung" (corps communication battalion), which isn't modelled in WitE, and a "Korps-Nachschub-Abteilung" (corps supply battalion), which is modelled as truck pool.
Corps could have one or more support unit staffs attached, like "Artillerie-Regiments-Stab", "Nebelwerfer-Regiments-Stab" and "Pionier-Regiments-Stab". These staffs were also empty shells and commanded battalions attached by army or higher commands, typically heavy artillery, nebelwerfers, pioneers, bridge engineers and others. The numbers of attached battalions varied wildly according to the corps' objectives.
For instance the XXVI. Armeekorps, taking part in the siege of Leningrad, in the second half of 1942 had up to 8-9 battalions of artillery, heavy artillery, coastal artillery and train artillery, attached to the "Artillerie-Regiments-Stab 782" and "Artillerie-Regiments-Stab 818" and led by "Arko 113". In the first half of 1942 there was much less artillery attached.
GBS: I wish there was an easy way, I find it likewise annoying, but once you're through (usually around turn 10), you have to take care only of new units and unit withdrawals. I usually keep some assets in reserve, like heavy howitzers and heavy nebelwerfers, and attach them to corps, which have to crack tough nuts.