Is there a way to check if a public IPv4 address/Subnet was obtained through illegitimate means by a webhost?
Also, can outright IPv4 hijacking last for years or only for minutes/hours?
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To be able to advertise a network, you must have the cooperation of the ISP(s) to which you connect. Most will require you to own the network(s) in question, and they will refuse to advertise networks if you can't prove you own them. If problems are caused by an incorrect route to a network, an ISP will work rapidly to correct the problem because other ISPs to which it connects may cut it off.
Someone using a network that belongs to someone else is only hurting himself because he can't get to the legitimate network.
Based on you question about checking from a web host (client), I think you need to be more concerned about a DNS problem.
You can do a search at ARIN to see who the registered owner is for an IP http://whois.arin.net/ui/
As for hijacking, I assume you mean that someone just picks a public IP at random and starts advertising it for their own purposes.
If their local ISP is accepting any advertisements and not filtering them, the bad routes could potentially get propagated until they are filtered at some point.