Most if not all of the existing AHs were paid for through separate specific donations made by JWs in each circuit, donated before and during the AH construction. If WT had provided any funding, it would have been as a mortgage to make-up for any shortfall in the initial fund raising.
In the past, each circuit maintained its own financial accounts. Often, even after sending a substantial (voluntary) donation to WT, there was surplus which carried over to the next CA and was added to whatever was donated at that assembly. If an assembly received less donations, perhaps due to local economic issues, the carried-over surplus usually made-up for any shortfall.
It was a relatively good system until WT became greedy and demanded all money each circuit held in surplus. Now, a large donation to WT is built into the rate per publisher. If there does happen to be additional funds realized beyond the publisher's daily rate, that too is sent to WT as an additional donation. Calling the expense 'maintenance' or an 'assembly hall expense', is in reality, misrepresentation.