Just to make sure

Can anyone confirm that how far you are from the enemy when attempting to tame matters? (If you have an answer from before G14S4, make sure it's consistent with after G14S4.) Also, does how much HP it have play a rule at all anymore? Like, is the success rate increased by a small amount by it being damaged, but it's still tamable at full health? Or is the same regardless of health? And is it moving an automatic fail or is success rate reduced by it being in motion?