I'm not sure which "denomination" you are speaking of, but in the Episcopal Church, all parishes owned their own property from the time this nation was founded (mostly by Anglicans).
The property canon which said parishes owned their own property was illegally changed at the 1979 General Convention of the Church. According to the official record of that convention (White and Dyckman's Annotated Constitution and Canons of the Episcopal church, 1982), "there was no record of that resolution passing both houses of the convention" or words close to this. I'm quoting from memory here.
Like many secular legislatures, much legislation gets passed in the closing minutes of a legislative session of a church. Some of this is by design and so it was that the liberals in the Episcopal Church used this legislative logjam to surreptitiously pass a change in the church's property law. The new change said that from that point forward, all local parish or church property was now owned by the diocese. This meant that the bishop could now use title to the local parish's property as leverage to force (for example) conservative or traditional parishes to go along with the liberal changes such as accepting women priests or ordination of homosexuals. Unfortunately, most Episcopal parishes ceded their parish property titles to their liberal bishops and did not contest this illegal property canon change.
Many people subsequently left the church and started new congregations and began to worship in peace without the distractions of heretical bishops and unbelieving clergy. These folks did not start a new faith or church, rather, they simply continued to worship and believe in the same manner they had before except without the institutional apostasy and error.
At the same time, the liberal Episcopal quislings labeled these traditional folks as being is schism. Who really is in schism, those who've re-written the faith to accomodate themselves or those who left the apostate parent body in order to continue worshipping and believing in orthodox Anglicanism?
The Falls Church is but one of 6. The 6 largest-member Churches in No. VA, among them the Falls Church, Truro Church, Church of the Apostles, are all fighting this battle with Bp. Lee.
They have also refused to monitarily support the Diocese since the Robinson vote - so the Diocese is really hurting. We used to joke about how Bp. Lee was going to be driving himself soon. Apparently there's still enough money that he still has his driver. I guess since he has a propensity for using College kids, he can still afford them. Sigh. I was hoping for some personal pain for the Bishop.
BTW, it's truly disgusting to read that the reason Bishop Lee decided to vote FOR Robinson was that his wife asked him if he was going to stay in the 19th Century or "be modern", or somesuch words. THEN he came up with the justification for his vote, that he felt that the people of New Hampshire had the right to vote whomever they wanted for their Bishop.