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There isn't an enforced limit to the number of children an item can have, other than the total number of items, which is limited to an Int64 key (a VERY large number).
Actually the same Int64 limit would likely first be reached on the item keyword or item attribute tables, but again, this number is so large it is essentially infinity in this application.
Of course as the number of children an item has increases, the time to display them in the tree and/or related items pane will also increase. The amount of time required will also depend on the overall speed of your CPU, drive, and/or network, but should increase linearly and be consistent for any type of child item.
If you currently have an item with a significant number of children (500+), you can use the amount of time needed to display them to interpolate where this "limit" is for your scenario.
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