Which MMR will be taken when transferring from NA?

Solution 1:

According to the Server Transfer FAQ, your MMR will transfer over to the new server. However your rank will not - you'll have to play another set of placement matches.

It does not specify how the MMR is moved, exactly. The new positional ranking system has only been available for a few weeks. If the server you're transferring to also has positional ranks, then it will likely be a one-for-one copy of your MMR. If the server does not have positional ranks (such as the EU servers), then we don't know how the MMR is calculated. You will probably have to open a support ticket with Riot and ask them directly.

Solution 2:

As I only have one data point (myself), my answer may not apply to everyone.
However, I spent 5200 RP on a two-way transfer... for science.

I transferred my account back to JP and promptly got placed in a Diamond 1 average game, where my teammates were D4, D2, Master, Grandmaster, and myself; we went up against Master, D1, D1, Master, D2. You can confirm the match on Riot's website here. Just look at how out-of-place I was:

I won the match and got a provisional rank of P1 52LP, meaning that I cannot go below P1 52LP even if I lose my remaining 9 placement matches. Proof:

If it had taken the aggregate of my 5 roles, I should have been in a P3-P4 game instead, because my first placement for each role has been P4 so far. Also, as I was Gold 4 on the server last season, as you can see on my op.gg, the match could not happen had it been last season's ranking.

Thus, it must have taken my highest role ranking, which is currently D4.