We are using an Enterprise Architecture tool. As we expand its usage, we are being asked to model at increasing detail.  My question is if you use an Enterprise Architecture tool --- what do you model and where do you stop? Do you overlap with an IT Service Management tool?

I would not have overlap in data between an EA-tool and ITSM-tool, ERP-tool, CLM-tool, etc.

But I would mandate, that Master Data for the IT Domain is used consistently across all those tools - with a conscious selection of SoR/SoE. The tools doesn't need to be integrated - a manual check of consistency at regular intervals could do - decide your approach based on TCO and resource availability.

This is just an opinion. I inherited a team who had likewise been modelling at great detail - but it meant the information in the model was often out-of-date and so it was not useful. The principle we applied was "do not model information you can get from configuration management as actual system configuration data". 

Most EA tools also fully support design frameworks/modelling, which goes beyond EA. As long as the tool is a good fit for it, why not - but of course, "it depends" on many factors: is it the best tool for design as well? Do you need a full link with the architecture within the tool, or is the link supported through other means in the organization (such as naming conventions and frameworks to use).

The question however also seems to imply to me the demand "how deep should an enterprise architecture go". In that part, I would focus on those models that are sufficiently static that you don't have an overly extensive maintenance on it. In that sense, it is very important that you know what the ITSM tool offers/supports.

For instance, I wouldn't model deployments as part of an enterprise architecture if I can query the deployments from the ITSM (assuming you have a method in use at your company to quickly filter on that information).

I don't believe that you need to actively link the two. In my company, some people like to automatically upload artefacts/objects in the EA tool from the ITSM, but the auto-upload does not know of the frameworks and filtering to actually make it visually appealing, and the governance of this uploading still needs to be properly tackled.

We use TOGAF (The Open Group Architecture Framework) as our EA methodology and framework. TOGAF helps us understand, design, and implement our enterprise structure and processes. As we deeper dive into modeling, we determine the granularity based on TOGAF's guidelines and our specific business needs.

While TOGAF provides a comprehensive approach, we ensure there's a distinct boundary between it and our ITSM - Service Management tool. This distinction helps us maintain clarity and avoid potential overlaps, ensuring each tool serves its specific purpose efficiently.