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Reviewing all the comments carefully. OG is by far the easiest tool to use for "swimlane" diagrams. For reasonably modern ones, you will need to use several different Stencils, and Insert a reasonable number of graphics or images. Cartoons are cute, but for professionals who want to draw Roles or Actors, a couple of good standards already exist, and those would simply be used in the "storyboard" or "scenario" "lane". "Swimlanes" are not new by any means, they are merely a horinzontal or vertical categorisation (in columns or lanes) of responsibilities (Actors, Roles). Now what you put in the lanes after that is pretty much up to you and the expected audience: you can keep it technical and standards-oriented or you can make it quite friendly and cute.

The point I am making is that the "swimlane" diagram is not a type of diagram, for which there needs to be, or can be, a native implementation. The diagram is a composite of other formal diagrams, which have specific types, laid over "lanes". And those specific types of diagrams already have perfectly good tools. Hell, you can make one of the lanes a timeline for budget or project approvals (and then we are approaching a Project Plan).

The only feature that is "missing" is OG (that allegedly exists in Visio), is the automatic re-sizing of the "lanes". Personally, I cannot see the "problem": either re-sizing the "lanes" to fit the new set of objects, or resizing the group-of-objects to fit into the "lane", is really really easy in OG. The lanes would be a layer beneath the objects in the lanes. There are various things to consider, such as whether the resulting text is comparable to the other text on the page; the error of changing the size of symbols; etc, so really, I would want to do that myself anyway, and avoid having it done automatically for me.

Sure, if you keep resizing the lanes all the time, and it is a pain, then evidently you have not drawn each original integral diagram (flowchart, process flow, etc) correctly or completely; you need to do that first, before you can use such in a composite diagram (such as "swimlane"). It is a problem in the way you are working, not in the tool.

There are lots of other features that I would prefer Omni addresses before they address the requirements identified here. And that is if someone can actually define the requirement, which is not clear yet.

The way I would describe it is, we need an attribute on a target object or group, that let's us "pour" any number of objects or a group of objects or text into the target object, and:
either resize the target object to contain the unchanged total size of the source objects
xor resize the total size of the source objects as a group, to fit into the target object

For me, it is no big deal to review the entire doc and do a bit of both, to maintain the overall context and relative object sizes. But I would draw the source diagrams completely, first.