I'm not aware of any maximum - there could be one that I haven't encountered. The most I've done was 19000 points in a single day.

I do however recommend that you don't do too big of a transfer in a single transaction. A few days ago there was a malfunction on Worldpoint's website which resulted in points deducted from Worldpoint balance while giving out an obscure error on the website (and no points deposited to AP). It took people several phone calls and a few days for Worldpoint to get that corrected (and points eventually deposited into AP).

When it works correctly, the points are transferred into AP instantaneously. You can log into to AP immediately after the transfer and see those points there.