An interesting situation

[neilwilkes]

I am in control of the Nordic Federation, and it would seem that I have a claim on the EU.
The EU is however controlled by The Academy.
What happens if I federate with the EU?
Would this give me any control over the EU in the long run if I hang on until I can actually Unify, or would it work differently somehow?
I may create a game save with this as a split point...just to see what happens...but it would be grand to know just what might happen

[DarthVicious]

Spoiler I suppose. I figured some of this out by trial and error, and there is a lot I have not figured out yet.

Spoiler: show

The chance of the EU accepting your offer to federate is controlled by whoever is sitting on their control points.

If the academy hates you, no way they will accept.
Same for unification.

If you own the executive control point, you can accept federation and unification. Its actually automatic.

If any of the other control points are shared, then the faction that owns those points may end up with a control point in your newly unified nation.

Note that miltech, gdp/c, and other stats will be averaged based on population. Unifying with a much lower stat nation can be a downer. In such case better to militarily conquer them.

[PAwleus]

If the Nordic Federation has no claim on the capital of the EU (and they usually don't) then they have no option to unify the EU (but the EU could unify them because they have or they could have claim on the capital of NF) even though you can federate the EU as the NF.

Click on the Executive Authority icon of the NF (in the upper-right corner of the NF window) and hover your pointer over the Ally column of the EU and you will see what are their unification conditions.

[neilwilkes]

If the Nordic Federation has no claim on the capital of the EU (and they usually don't) then they have no option to unify the EU (but the EU could unify them because they have or they could have claim on the capital of NF) even though you can federate the EU as the NF.

Click on the Executive Authority icon of the NF (in the upper-right corner of the NF window) and hover your pointer over the Ally column of the EU and you will see what are their unification conditions.

The first part of your answer has answered my question - many thanks.
The second part I am aware of - but oddly, since I unified with Denmark into the Nordic Confederation, all options to federate with the EU had disappeared after running the National Policy mission - yet the option to federate was definitely there when I federated Denmark.
Not to worry though