For centering without a lathe, mark center with machinist square, center punch, either drill both pieces for a tight fitting small pin to help keep the first weld tack from pulling off center, (or counter bore the spline with borrowed lathe as already suggested). After tacking lightly in 3 or 4 spots, tap with wood block and hammer to get it true. A couple of V-blocks clamped up and dial indicator can help if you don't have a lathe. After welding, recheck for true. If it's not, you can heat it to red and wail away with a hammer (gently) to true it up.