It's been bothering me for a while. I know they can't find him in Grimmauld Place, but why can't the Ministry find him while he was on the run in the 4th book?

I mean, owls find him instantaneously, so why can't a government of thousands find him?

Initially I thought that "JKR has already answered this one", she explained that wizards and witches can make themselves unplottable. The explanation would make sense. Also agreed that ministry must have tried to find him and concluded that he was unplottable and so chose different tactics.

But it's also true that he was found out by Hedwig, Pigwidgeon and at least three school owls, not to mention the tropical birds and the way Dumbledore communicated with him. Similarly, Hedwig was able to locate Ron/Hermione in a place under Fidelius. In each instance the birds did not know where the person was. In the event, a witch or a wizard or a building is unplottable, how can the birds actually find them out? Are there different degrees of "unplottable"? For instances, witches and wizards may decide to make themselves selectively unplottable and allow those with no harmful intentions to find them. Sirius could have done that and allowed himself to be found out by Hedwig and others once he sensed her. But then it would not explain how the school owls found him. Similarly, Hedwig may have been allowed access to Grimmauld Place. There's much that can be debated here.

Interesting question. Of course eventually the ministry is intercepting owls so he tells Harry not to send Hedwig. Harry does tell Hedwig not to come back until she finds Sirius. It takes her a long time to come back with the response, but JKR doesn't explain how the owls are able to find someone who has made themselves unplottable. Perhaps there is some type of network that only the owls are able to use, and they communicate with each other to find unplottable people. I know that Sirius breaks into a wizard home to use the flu network to communicate with Harry in GOF, but I am not sure how the owls know how to track someone down. Remember too, in SS the owls were able to track Harry to that house on the sea that Vernon takes the family to and the hotel that they stay in prior to that, so there must be someone inter-owl network that the owls can track people down when the ministry cannot.

^^ The point is that if owls could track wizards or witches who had made themselves unplottable, then what prevents ministry from tracking the same witches or wizards using their own flock of owls. JKR on her website says that if it was that easy to locate Tom then the ministry would have send him an owl and followed it. This would suggest that those who are uplottable should not be found out by owls. However, Sirius was found out not only by Hedwig, Pigwidgeon and the tropical birds (whom he was all familiar with), but also by owls from Hogwarts who he did not recognise. Thus, even allowing for Sirius spotting them in a distance and somehow allowing them access does not make much sense here, since owls would have been able to track the general vicinity, which does not help someone who's unplottable. Owls were able to locate Harry due to the trace the ministry puts on underage witches and wizards and he was not unplottable then.

Good point, but perhaps it has something to do with the fact that Sirius is an animagus, and that makes the ministry unable to track him. He is not registered as an animagus, so that is how he was able to escape from Azkaban. If it were that owls could find anyone who was unplottable, then the ministry could have easily found people in the Order as well, when they were at Grimwauld place. Perhaps there is some way that you can make yourself taboo to certain owls, ie: Hedwig, Pigwidgeon(whom he sent from a post office to Harry), and owls from Hogwarts. There maybe a way that he could make himself available to be found by only certain owls, and not others who did not belong to either Harry or Hogwarts. Just my opinion that there were only the owls of the school, Hedwig, and Pig that were used to contact Sirius, so there must be some kind of charm that would make those particular owls safe to use to contact him, until the ministry began intercepting such owls.

Fair point, it does make me wonder. But what I think is that it is part of animals' 'super intelligence' almost. Like how animals can tell when a natural disaster is going to happen like earthquakes. (Take for example the recent Kent earthquake in England. An hour before all the dogs in Kent started barking for seemingly no reason.) Perhaps owls are very intelligent creatures and can locate people even when people can't. Perhaps it is like an owl 'sixth sense'.

Alright, I like this question. It does make alot of people think. I think the reason Owls can find Sirius or anybody is because they have there "senses" which make it easy for them to find a person. Also, Witchs and Wizards can make themselves un-plottable which is hard for the ministry or anybody to find them.

Ok

But if it were so simply, it would be enough for the Ministry to send an owl to Sirius and some Dementors following it, so they could catch him.

So, I guess there must be some kind of magic explanation, maybe Sirius let Harry's owls to find him or something like that.