Do LevFin bankers typically have their own clients?

At the senior levels, I'm wondering if product bankers typically have their own clients (esp. LevFin) since it seems like vast majority of the time, they seem to be merely executing deals that the coverage bankers originate. But even the execution seems to be mostly run by the VPs, which begs the question: what the heck do LevFin MDs do anyway?

I can imagine how DCM have their own clients since their deal flow is frequent and consistent, so it makes sense that the company treasurer/CFO bypass the coverage person and go straight to the DCM person as the point of contact. However for a product like LevFin, where the vast majority of deals are event-driven, wouldn't the vast majority of the deals in that space come via the coverage/sponsors MD's idea generation?

Which leaves the question: do LevFin MD's typically have their own clients, or do they mostly just piggy-back off the coverage group's origination? Do LevFin MD's typically have less clients than their coverage counterparts? How do LevFin MD's get evaluated in terms of revenue generation (for their comp) if the vast majority of their deals are just piggy backed off of coverage?