There are a couple of factors that should play a role in the number of eDiscovery Centers you wish to create. How many search service applications are there? What content each of the search service applications will crawl?
When there is only one search service application that crawls all of the sites that have discoverable content, you have a single eDiscovery center. If there are different search service applications that crawl various subsets of the discoverable content, then you have multiple eDiscovery Centers in place.
Associate eDiscovery Centers with search service applications allow for discoverable content to be crawled by a search service application that is associated with an eDiscovery Center.
A search service application gives you an on-site SharePoint farm that can’t crawl the content in SharePoint Online. If you have discoverable content in SharePoint Online, you also need to create an eDiscovery Center in it.
An eDiscovery Center must be in a web application that is able to support claims authentication in the farm that is hosting the search service application. For each eDiscovery Center, make a record of the farm that will contain that eDiscovery Center and the search service application that is associated with it.
Once you have determined the number of eDiscovery Centers you will have and where they will be located, you can identify the content that each of the search service applications will be able to crawl. To be discoverable, the content on share files must be crawled by a search service application that is connected to the eDiscovery Center.
It is possible to manage the discovery of Exchange Server 2012 content from a SharePoint 2013 eDiscover Center. To do so, you need to configure a search service application that includes Exchange Server 2013 as a result source. If you would like to manage the discovery of Lync Server 2013 content from a SharePoint 2013 eDiscovery Center, you need to configure Lync Server 2013 to achieve content to Exchange Server 2013.
In order to manage discover of Exchange content with SharePoint 2013; you have to use Exchange Server 2013. In order to manage discovery of Lync content through SharePoint you must be using both Lync Server 2013 and Exchange Server 2013.