The most complicated part of the system is figuring out who has access to do what, as everyone is adding to and updating the same tree. Below is what the system is setup to do, intended to provide enough flexibility and security, but not be too prohibitive.
Anyone who is logged in can add an unconnected person, and becomes the moderator or owner of that record.
If you are the moderator of a record, and of that person's spouse, parents, or children, you have unlimited access within those records to update the information and linkages as you like.
This is to try to provide a little more security, so that you can't just go to any record that someone else posts and add onto it. Instead you start with information you have already entered, and link out to other records from there. For any records that you do add yourself, you can add children, parents, and spouses, or link to anyone's children, parents, and spouses directly from there.
While browsing, avatar icons may show in the lower right of each person's parents, indicating your moderator access for the parents. This will not show if you are viewing your own people, and you are also the moderator of the parents -- this would just be cluttering up your screen. But they do show if the current person and the parents belong to different moderators. You can also choose to show the avatar icon for childen, under My Account > What I See.
Here is a summary of what you can do:
For the cases where you and other researchers both need moderator access to unlink a relationship, you can suggest the change to them, or they can suggest to you, and then the change will be made when the moderator accepts the suggestions.