There’s no the Rothschild mansion

There’s no the Rothschild mansion, per se. As another answer explained, it’s a pretty sizeable family now. They have Austrian (or at least they used to?), German, French, and British branches, and now with James & Nicky, the start of an American branch. Members of the prominent family over the ages have built their own impressive estates, some demolished, some still intact. Palais Albert Rothschild - Wikipedia, Vienna, Austria. Built between 1876 and 1884, demolished in 1954. Château Rothschild - Wikipedia, Paris, France. The since-abandoned mansion is in a state of disrepair and decay, but it’s been said that a restoration project will take place starting this year (2020). Living members of the French branch of the family have presumably moved elsewhere. Waddesdon Manor - Wikipedia, Buckinghamshire, England. Constructed between 1874 and 1898 for Baron James de Rothschild, the palatial estate and its contents has since been bequeathed to the National Trust, and managed by the Rothschild Family Foundation. If I recall correctly, they routinely have a farmers market before the Covid-19 crisis came around. Ascott House - Wikipedia, Ascott, England. Not too distant from Waddesdon Manor, the architectural style of the two estates contrast considerably. Sir Evelyn de Rothschild, financial adviser to the Queen, is said to still live here with his wife, Lady Lynn. Mentmore Towers - Wikipedia, Buckinghamshire, England. The Jacobethan estate was built between 1852 and 1854 for Baron Mayer de Rothschild. This house has been used as a setting for several TV shows and films, perhaps most notably in “Batman Begins” (2005. Dir. Christopher Nolan), as Wayne Manor. I actually don’t know what it’s used for today. Other living members of the family may have purchased their own properties elsewhere, but probably none as impressive as the ones listed above. And why would they? Maintenance of sizeable buildings are generally a financial nightmare, and a family as historically financially-savvy as them may prefer to allocate their funds elsewhere i.e. philanthropic pursuits or investments.