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I usually give a bit more info on my side. Hi - I'm researching x person who I think was my ... And then I ask a direct question. I tend to do research in intensive boughts, so I might reply a bit later.
also remember to check when they were last on line some people put a tree and then forget about it. some people work in a library so log on every so offen. others take a break when real life get too much and remember they might not related to anyone in the tree you are interested in.
the best thing to do i find is say i am interested in xxx in your tree (name the tree if they have more that one up) and then say why? ( he is my grandfather etc) the big thing is family history is patience. new records come on line all the time and new people get interested put up trees. I have reply to message board on ancestry that were posted years ago and i still have got replys and help and info
A lot of people have uploaded stuff and haven't really been doing anything active for a while, and may also miss message notifications. When I last logged in I had 3 or 4 unread messages going back over the last couple of months (I did reply to them all and apologise for delay, though).
I agree, though, that giving a bit of background information and asking a direct question is often best. That way you don't come across as "Hello, I have been researching my family for five minutes since I saw a repeat of Who Do You Think You Are and I want you to hand over all your research that took you years. I won't really understand or appreciate the sources you've cited or that unsourced suggestions don't carry equal weight with solidly substantiated events, and I'll indiscriminately merge your data in with low-quality stuff that I've got from anyone else who will answer me."
I agree with others here. You need to provide detail and essentially demonstrate your own credentials. You need to sound articulate, and genuinely interested in the people/relative concerned, and not like a name collector. It also helps if you can specifically offer them some information too, but is not essential. I say something like "I'm researching X who I believe to be my blah blah blah, and I'm related through my maternal father's line/my grandfather's brother etc. I'm interested in them because xyz, and would love to share my research with you, do you have any further information on abc in relation to them?"
I've had loads of messages from people who're interested in/offering info about people I'm only very, very distantly related to. Comes of having far too many people on the tree, of course and being addicted to adding more! Had a similar experience as you with a distant cousin in Australia. This chap clearly only had limited access to the site and asked for information on his ancestors in the UK, which I dutifully typed up (all 16 pages of it!!) in narrative form. Haven't heard from him since I emailed it all over.