@Brenton J Gowland 

till now there is no option to do this with a MindMap you created in miro - even not if you lock the branches - they are moving …

So three things could be done:

Create a wish and vote for this:

https://community.miro.com/community-welcome-guide-14/wish-list-everything-you-need-to-know-1099

Generate a ticket for the support team: That even if you lock the branches they are moving (this should not be - if you lock them they should keep locked):

https://help.miro.com/hc/en-us/articles/360020185799

Create your MindMap with the Sticky Notes using the Bulk-Mode:

https://help.miro.com/hc/en-us/articles/360017572054-Sticky-Notes#h_01EWMZS3NDPZ1X6HXQYGCVFJM5

after that you use the arrows to bind them together.

From a layout mode you are more flexible to create whatever you want:

Michael

@Brenton J Gowland - Can you please clarify what you mean by Auto Layout? If you are referring to this Auto Layout, there is no way to “switch it off”.

Auto layout

Align and distribute widgets on your Miro boards quicker than before with auto layout:

1. Select the widgets you need to align.
2. Click on the grey icon in the upper right corner and drag it horizontally.

Taken from the Structuring Board Content Help Center article:

https://help.miro.com/hc/en-us/articles/360017730973-Structuring-Board-Content#h_01ENWJZZ8QX1GK0EE18CHS66G7

While I am here, the only other thing I can think of that you may be referring to is “grid” mode in frames, where objects “snap” into place. If this is what you are referring to, then you can set a frame to freeform layout.

Grid in Frames 

Working on a user story map, service blueprint, customer journey map etc., you want a quick way to organize objects and keep them organized after adding new ones. In cases like this grid in frames comes in extremely helpful.

To automatically snap content in the frame to a grid, enable the Grid option in the context menu. To switch back to the free-form layout, choose the Freeform option.

When you drop a new object into a frame, it is arranged along with the other objects in the grid. This is a real time-saver for those who often add new content to their boards and need to keep them in order. Resize the frame to change the position of objects in the grid.

Please note that links, comments and other frames cannot be snapped to a grid.

For more on this, see the Frames Help Center article.

@Robert Johnson It seems the Grid option has vanished from the context menu for frames. That is really sad as I was looking for exactly this feature.

In fact there is one way to prevent auto movement. Just treat your topic as a new mindmap and connect them via connection lines. This will give much more freedom. Moreover, it is not necessary to treat all offsprings of all levels as a mindmap, just do it with big branches where you start to feel uncomfortable with auto adjustment