Thanks for your sympathy over the ubiquitous and extensive puddles of pee which have overrun my home since Marie has stopped wearing nappies. Bearing this situation in mind, I'm surprised you want potty training advice from me but I'll do my best.
We had it pretty easy with Fraser. He has a bladder the size of Iowa and sphincters of steel. We ended up having to toilet train him because he was holding it in for seventeen or eighteen hours at a time and then peeing his nappy off with the explosive power of a Super Soaker. It was useful for putting out small fires but ultimately more messy than teaching him how to use a potty. The main problem we had with training him was actually getting him to perform. He had to be sat on the potty for ten minutes being constantly entertained with stories about Teletubbies before he was able to relax enough to release the floodgates. Once he got the hang of it, though, he only needed the toilet twice a day and barely had an accident. He went from thinking a potty was a funny kind of hat to no nappies whatsoever in about ten days. Easy.
Lewis wasn't much harder. He got the hang of using the potty really fast. All that was needed was to sit him down and close the bathroom door and he performed. Bizarrely, he then wanted to stay there for ten minutes being constantly entertained with stories about Teletubbies but at least the primary goal was always achieved quickly. Closing the bathroom door seemed to become a trigger, in fact. We discovered this one day when he took his pants down and closed the door himself before sitting on the toilet. (Nasty).
We thought he had a smaller bladder and needed to go more often so we had him in pull-ups for a while because he was more prone to accidents. Then, not long after he was in normal pants, we went down to my parents by train and he decided he wasn't going to the toilet again until we got to granny's. He decided this at the station in Edinburgh. My parents live in Norfolk. This did not seem like a good idea... We were nervous... We kept taking him to the toilet but he refused to perform for the entire six hour journey to Norwich. After that, it was another forty-five minutes in my parents' car. Their new car. The kind of car that has a TV to show you where you're reversing... We were nervous... But he made it all the way to their house without so much as a little dance. Go figure.
We didn't worry so much about taking him places after that. Except to get his shoes checked. Something about the prospect of new footwear seemed to irritate his bladder. For months he was bound to wet himself within twenty-four hours of visiting the children's shoe department of John Lewis. And I don't mean a little accident where he needed fresh pants, I mean the kind of accident where I had to stuff his trainers with newspaper. On the occasions where we'd actually had to buy new shoes, this was somewhat annoying.
The boys were both pretty keen to get out of nappies. Given the opportunity to use the potty and plenty of encouragement when they tried, they responded quickly. Marie just hasn't been so interested. We considered a chart where she would get to put on a sticker every time she succeeded in using the potty but she's the kind of kid who would abuse the system and end up producing a tiny amount every ten minutes just to get a sticker. Instead, we cut off her supply of Numberjacks if she refuses to go to the toilet every hour or two. This has worked reasonably well and she's getting the idea. The frequency of mishaps has calmed down but we're still getting up to three a day. Their scale has also reduced because she's keen not to be hosed down in the shower. We'll get there eventually. We know she can do it because she's going dry overnight. She just needs to apply herself a bit.
Some of her new pants have numbers on and this is helping to concentrate her mind. She mutters to herself, "Numberjacks for watching. Not for peeing and pooing on." Can't argue with that.
Every child is different. Good luck with Sam. I'm impressed he can write his own name already. Hopefully he'll stop doing it in such an unfortunate fashion on your clean laundry soon.
Yours in a woman's world,