How can I add emails of people without giving them permission to edit?

No. Once they fully claim their profile by setting a permanent password they own their own profile hand have full edit access, but hey can open up for giving family full access to edit their own profile.

Does it matter?

You are by the way not removed as manager, - the list is just hidden an will be restored if the profile get unclaimed.

Bjorn - sometimes you simply stop showing as a Manager -
But sometimes in the Revisions Tab it explicitly says you were removed as a Manager - does the latter still just mean the list is hidden, and you will be restored if the profile becomes unclaimed?

Yigal -if they set their password, they being the only one who can edit their profile is the default - and they cannot choose to have you be the manager instead - tho they (and you!) can choose to allow family to edit their (your own) profile
Also - anyone can edit any profiles in their Max Family and, if you are in their Max Family, any Private Profiles you manage.
You can limit them somewhat in that regard by blocking them - but unless they are doing something majorly wrong or contrary to your wishes, seems wrong to invite, then block.

So if I want to keep ownership of my tree, the best practice should be not to invite others
?
From what I have seen, most people set a password, and forget it not to be used again

I would think that registering email and gaining ownership should not be linked

Lois, - you can be removed as a manager on profiles by a family member of that profile where you are not a family member. Fair enough if you goes to close onto other users outside your own family with your duplicates, - they have access to kick you out. On the other hand you can do the same and also add your self as manager on profiles added by others within your family without asking for approval.

Personally I have a big problem understanding why having your own name or not having others name on profiles is so important if the line is correct and you don't need full edit access to correct anything. I would have preferred that manager names is not listed at all because that brings the focus away from genealogy.

Yigal - if having a personal tree where no others have access is important for you Geni is probably no the correct site for you. The main goal from day one is a world tree where everyone collaborate together to build a world tree, which of course involves that other users have access to contribute. Do not fear edit wars if profile facts is based on sources.

Read more about the Geni goal: https://www.geni.com/worldfamilytree/learn-more

Bjorn - sorry I wasn't clearer. Yes, I know folks can remove anyone from Managing a Profile in their Max Family if the person is not also in the Profle's Max Family. Not what I was referring to.
I was specifically referring to instances where the revision tab message said I was removed by the person claiming the Profile.
I knew I would disappear from the list of managers if they added their password -- was wondering if that was all that happened, or if they had been super-ticked to see I had been a manager and kicked me off before doing that, or ??

Yigal - since Profiles and Trees can be merged, if you want to "keep ownership" of your tree, as Bjorn says - you almost certainly want to work at a different site.