If I pay real estate taxes on a vacant home in new jersey, will the home eventually become my home legally? There is not mortgage.

Yes, as Ms. Anderson says, you may have a tax lien on the property but only by going through the process of a foreclosure and sheriff's sale could you be eligible to obtain ownership. But the actual owner may also redeem by paying all the outstanding taxes (you say there is no mortgage, so it is likely that the house is worth more than the amount of taxes owed).