He wrote the story with his friend's 'assistance'. = He wrote the story 'with the assistance of' his friend. [=his friend helped him to write the story]
Our family had to 'go on public assistance' [=receive money from the government] when my parents lost their jobs.
Nobody 'came to her assistance' [=nobody helped her] when her car broke down.
(..) Thought you'd like that. No, not really. Not this time. I would rather suffer the end of Romulus a thousand times, I would rather die in agony than accept assistance from you. You've got it. Arm phasers. Fire everything we've got. Yes, sir. - Sulu, let's go home. (..)2009 Star Trek
(..) - Aye. This is captain James T. Kirk of the USS Enterprise. Your ship is compromised. You're too close to the singularity to survive without assistance which we are willing to provide. Captain, what are you doing? Showing them compassion may be the only way... to make peace with Romulus, Spock. (..)2009 Star Trek