When logging into the app fresh on an iPad, there are multiple places where the initial state of the split views require optimization:
After creating a new account without adding or creating a site, this is how the "My Sites" tab looks like.

Fyi @frosty, @rachelmcr
Tested and confirmed that the My Sites screen on iPad for an account with no sites displays the "Add new site" prompt in the sidebar on the left which looks a bit odd on iPad screens.
Create a new site for your business, magazine, or personal blog; or connect an existing WordPress installation.
Add new site
Portrait|Landscape
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Tested with WPiOS 15.4.0.1 TestFlight beta on iPad Mini 4 (WiFi) (iPad5,1) iPadOS 13.6.
Thanks @designsimply and apologies I didn't loop you in!
While beta testing the Unified Login & Signup call for testing with WPiOS 15.7.0.1, I noticed that the Notifications > Install Jetpack prompt also displays small and to the left in contrast to a similar prompt in Stats where it's shown on the right.
"Install Jetpack" prompt in Notifications|"Install Jetpack" prompt in Stats
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Tested with WPiOS 15.7.0.1 TestFlight beta on iPad Mini 4 (WiFi) (iPad5,1) iPadOS 13.6.1.
(internal reference: pbMoDN-15R-p2#comment-2389)
Updated title to reflect that this covers multiple issues.
Notifications: on initial login with no notifications present, initial content is shown in small left pane. Content is offset down for some reason, and the right pane just shows gray.

@osullivanchris @frosty -
Regarding the layout when there are no sites:

Technically, this isn't broken - it's always been this way*. That is, the NRV displayed in the left pane with an empty right pane because there are no site details to show. Since there's nothing to "fix", I'm not sure what we want to show here. The no results view is displayed in the left pane because there are no site details to display. If we move the NRV to the right pane, what do we show in the left?
*Except for the NRV being off center vertically. That's is an issue, but unrelated to this.
Update:
This applies to Notifications as well.
The left pane shows the list of Notifications, the right shows notification details.

When there are no Notifications to show, the NRV is displayed in the left pane with an empty right pane (because there are no details to show). Same question applies - if we move the NRV to the right pane, what is displayed on the left?

Thanks for clarifying, @ScoutHarris. I _thought_ that previously if there were no sites, we would display a single full-width view containing the no results view. I think I looked into this and there was still code to adjust the width, but it didn't seem to be having any effect any more. I think notifications could potentially be the same – display it full width if there are no notifications to select.
That said, our split view code is now very much in the realm of 'here be dragons' (and I wrote it! 👀), so this may be easier said than done...
To recap a Slack convo with @frosty -
Noting https://github.com/wordpress-mobile/WordPress-iOS/issues/15019 - No Sites view: view disappears when rotating on iPhone with split view.
It's not an iPad issue, but it is a split view issue.
Hey @frosty .
I looked at the My Sites NRV for the better part of 3 days, and I cannot figure out why it's not full width. From everything I've read, it should be working. But for some reason, the width is "stuck" at whatever it was initialized at and refuses to change. For example:
I did notice a couple of other issues during my adventure.
emptyViewController set in Blog List's initialDetailViewControllerForSplitView so it cannot be seen anyway. I worked around/fixed this by returning nil instead of an empty VC (setting no detail VC). I haven't submitted a fix for this since I can't get it to show full width correctly. I do think this is at least partially responsible for the issue I noted above (https://github.com/wordpress-mobile/WordPress-iOS/issues/15019 No Sites view: view disappears when rotating on iPhone with split view).At this point, I'm stumped on the width problem. If curiosity gets the better of you, feel free to take a look. But for now, I'm going to move on and look at other issues to maybe have _some_ success.
Another "not iPad but split view" issue:
https://github.com/wordpress-mobile/WordPress-iOS/issues/15067 - Notifications > Jetpack install prompt: view disappears on rotation
This is to summarize the state of this issue after my poking around.
The root issue still remains, that is when an empty view is displayed that is meant to be full width, it is not. This includes:
If you have some Notifications, selecting a filter that has no notifications will display the 'No notifications' message in the left pane. This is correct behavior.
I was unable to determine the root cause of full width not working. As noted in my comment, the column widths just don't update after initialization. To resolve other issues this was causing, I added a workaround to just not attempt full width. This should be removed when the root cause is resolved.
Remaining issues:
Resolved issues:
Most helpful comment
Thanks @designsimply and apologies I didn't loop you in!