For the last 2 weeks I have seen this dog at the park where I take my boys to feed the ducks, he always was sitting by the grounds keepers' hut.........(long stort short) he followed us home today,  went back to the park to find who he belonged to(no luck), so I took him to the vet (no id chip - just a black collar without a tag), I've put some found sign around the area, should I keep him with us till his people are found or should I take him to a shealter?

He is a nice friendly dog, I think maybe a GSD mix

Hard though I'd find it - with young children in the house, I wouldn't risk it. A dog may seem friendly when it's to his advantage, but once you get him in a house, and he feels trapped or gets his 'feet under the table' you may find he's a very differnt dog. If you can get a lead on him, can you take him to the local rescue?  They will probably take your details and will asses him, they may well find he is truly of sound temperament and if asked will contact you if you want to give him a home......

You should contact all the vets & dog wardens in your area and the police to notify them you have found the dog and what you intend to do. Many owners will when their dog goes missing contact the vet to see if anyone has brought in an injured dog. They will usually contact the police and sometimes dog wardens. Leave a good description or picture with the vets, police and wardens, if you can.
When I found a dog wandering in the road, (and having seen it have a near miss hit by a lorry), I managed to catch him and take him into my house. I notified the police, dog wardens, and vets. Then to make sure I found his owners, I put up posters and advertised that I had found the dog on the main road on the local radio.
His owners did turn up but it seems they were the "caring type" who allowed their dog to run loose all day, and he often went awol for days after bitches in season! They seemed t think this was ok and natural behaviour!