Sitecore Managed Cloud provides a hosting service for the infrastructure associated with Sitecore. The entire topology is owned and "managed" by Sitecore under their Azure Subscription. Generally, the definition of this topology is based on the agreement between the client and Sitecore. From what I have seen, this usually consists of 3 environments (DEV (XP Single), STG (XP Small), PRD (XP [based-on-traffic]). Keep in mind, once you get to scale, the size of the topology usually just drives [expected] CD count.
From an ownership perspective, the contract usually includes some level of monitoring or support, and Sitecore is responsible for security/access management; when someone needs access to the environment, I typically have to submit a support ticket with the MC Contract Identifier and list of emails addresses to have them added.
From a support perspective, the line grays a little bit. I am a contributor for the MC instance that I worked on, which means I have access to do everything except manage access. I have been able to redo the topology to fit my client's needs (e.g. switch to an elastic pool, increase CM tier, etc.). Generally speaking, the partner plays a large role in supporting the applications, as they are responsible for adding, breaking, and fixing the code. If there are infrastructure issues, then a ticket can be opened with Sitecore to have them examine it. However, it might be faster to figure out and resolve the issue yourself; it depends on the severity of the issue and the SLA on the MC Contract.
Ultimately, the contracts are usually based on annual Azure Spend (billed monthly). The client has a spending limit, and if they go over that (unforeseen scaling === more CDs === more money), they can be charged overages. Keep this in mind when making or suggestions any infrastructure changes to the client.
Ultimately, Sitecore is really just providing a hosting platform, and the support model ends up being along the same lines as a standard Sitecore + implementation partner implementation.