Quote Originally Posted by iCake View Post
Okay,
Он вышел из дома, отправив письмо ----- He left the house after he had sent the letter or He left the house after sending the letter (отправив --- completed action already)
Он выходил/выходит/будет выходить из дома, отправляя письмо ------ He was/is/will be/ leaving the house while sending the letter (two simultaneous actions) (отправляя --- the action is still in the proccess)
Он выходил из дома, отправляв письмо ------ He was leaving the house while sending the letter (two simultaneous actions as well) (отправляв --- the action was still in the proccess at some moment in the past)

About the last example, I don't even think one can use the word отправляв, because I'm not sure it's the word at all. Он выходил из дома, отправляв письмо just sounds really strange. I personally would say Он выходил из дома, отправляя письмо.

So I just showed you what the word отправляв would be if it's a word.
I don't enjoy bringing up the same issues on and on but when the topic is difficult I don't have an alternative.
I found the expression: "She run on me, asking for help".
I have to choose from three adverbial participles which is the most suitable for this expression: прося, просив, попросив .
Based on what you said I have the three following alternatives and an attempt of translation
1. Она вбежала ко мне, прося помощи = She run on me, (while) asking for help. This it means that she was running on me and at the same time asking for help. As iCake mentioned this is for two simultaneous actions
2. Она вбежала ко мне, просив помощи = This adverbial participle as I understood it is not used in Russian (I found it in all tables of Wiktionary for the majority of verbs), so I will not give a try to translate it.
3. Она вбежала ко мне, попросив помощи = She run on me, (after) asking for help. This does not make sence based on your explanation iCake and I shouldn't use it. Correct?