When people talk about adoption in Procure-to-Pay they generally mean "user" adoption as measured by the proportion of requisitioners using the solution or possibly the percentage of total spend managed through the solution. I have two issues with this.
First, measuring the breadth of requisitioners and the amount of spend going through well managed P2P solutions is a very good measure of the success of the solution. In fact, it should be a major factor in evaluating prospective P2P solutions for your company. Problem is, measurable and comparable metrics are hard to come by. My sense is that P2P vendors don't have great things to show here and (for those who do) may worry that past successes would raise expectations and mess them up down the line (especially if they are SaaS vendors who need to continually beat expectations). Like the safe harbor statement on a mutual fund prospectus, "past performance is not a guarantee of the future" rings at least partially true when adoption is considered. Company cultures and senses of urgency can differ widely and affect relative rates of success. On the other hand, past failures may have spurred some interesting and ultimately successful new adoption strategies (especially, again, in the more nimble SaaS solutions).
Second issue is on the scope of what we call adoption. P2P seems to point toward the amount of spend and a whole raft of different users whose adoption you want: requisitioners, buyers, AP, Supplier/Contract managers, etc. Seems like a good broad set of stakeholders to go after, doesn't it? In fact, there is a often overlooked group that figure in as importantly as the above stakeholders, and as numerous as all of them put together! It's your suppliers. If you are approaching P2P as a closed loop process (albeit with lots of ins and outs), then suppliers are implicated in at least 5 places in that closed loop. This fact alone is what kills P2P as an ERP system add-on (because all your suppliers aren't users on your ERP system). But assuming you can get past that, the question remains: how are you going to get suppliers to adopt your new P2P system?
Force them? Think again. Your company pays 100% of the paycheck of your requisitioners, but forcing them to adopt is a losing proposition. At best, your company contributes 10% of your suppliers' paychecks, so your leverage is even less. Best thing I've seen work is the same thing that works in the consumer space: ease of use. Not just user interface, this means you have to be relevant to your users (buyers and suppliers) and they'll repay you with their attention.
So, it’s not an easy thing to get a handle on, but don't let that stop you from digging into this area of inquiry. Ignore adoption at your own peril. Ask vendors for metrics and then thoughtful discussions on those metrics. Then evaluate their solutions for how close they are to your own consumer experience on the web. If you are reading this you're already an expert on that.