How do you pay contractors?

I think I did something like 50% and 50%. Or in even thirds. I agree, paying too much too early is asking for the common problem of having the contractor lose interest and disappear. Personally, I'd be suspicious of someone even asking for those terms.

We paid 40% on signing, 50% 2/3 of the way though, and 10% when finished, but we'd seen two jobs by the contractors before, so we were more inclined to trust them.

This is what our architect told us: There would normally be a deposit of 20% due at the start of the project. The contractor would then issue applications for payment on a monthly basis. The amount requested each month will vary according to how much work has been done and there could be a bit of a range on the amounts from one month to the next, say from $50k to $200k. The deposit would be applied to the first 2 applications for payment.
In each application for payment, there would also be some amount held back that you would not pay to the contractor until the end of the project. This is called retainage and is usually 10%. Once the project reaches a point called substantial completion, then the retainage is reduced to some amount to cover the remaining work.