I was quite lonely as a child, so when I make a friend, I try very hard not to let them get away. I fear this might be smothering to some! I hate to lose touch with people I like/love. I like the description of friendship in "The Little Prince", though I guess it doesn't work for everyone, and is a bit impractical.
If I have decided unilaterally that someone is destined to be my friend, I will usually behave as though we know each other slightly better than we actually do - it generally works. But it is harder as an adult, to find times when they can meet you.
I think I am a bit dysfunctional as a friend. But I have friends from school, university, kids who lived down the road when I was at uni, from a goth club I used to go to in York, various gay scenes, past jobs in the photo-lab, Zoo and the Arts Centre, holidays I've been on, and fandom, and people I've met in cafes/at clubs. And I miss them all, and wish I could visit them all.