wealth is more centralized toward the rich than it has been since the gilded age.

This is strictly speaking not true but I will get back to it sometime later. There has been an excellent paper by Emmanuel Saez and Wojciech Kopczuk estimating wealth inequality in the United States in the period between 1916 and 2000. The authors have considered four categories: tangible assets (real estate, consumer durables), fixed assets (bonds, stocks), corporate stocks, income from unincorporated business and farms and subtracted liabilities (mortgages and other forms of Consumer debt) to obtain the net wealth of people at different quintiles. They have also included pension plans like 401-K, IRA and excluded benefits from Social insurance schemes like Social Security. There have been 2 other studies on wealth inequality that I have been aware of. There is the Survey of Consumer Finance Report by the Federal Reserve, and a paper by Sylvio Allegretto from the Economic Policy Institute but I will be considering the first paper for this answer.

It is important to start with the total wealth that has been produced in the country. Between the period of 1916 and the start of the World War 2, there was no increase in net wealth because a large portion of it was destroyed during the Great Depression. There was a steady and impressive increase during the portion between 1940 and mid-1960's and a marked slowdown during the period from 1970's till 1990's. There has been a similar trend noticed for growth in productivity (i.e the total amount of goods and services produced per person in a year) and income. Similarly, the composition in wealth held by the top 1 percent as changed. During the period between 1916 and 1930, around 70 percent of wealth was held in stocks as financial markets and the real economy boomed during the fast growth rate of 1920's when new Industries were created due to improvement in technique of labor, increase in stocks of machinery, commercialization of technologies and paradigm shifting management practices like Fordism and Taylorism. A comparatively underdeveloped financial perspective (from today's perspective!) meant that there was little scope in diversifying holdings and the stock markets boomed anyway.

In 1929, the top 1 percent held 40 percent of the total wealth which fell to 30 percent between 1929 and 1932 because of the stock market crash and general catastrophic economic situation. Their share continued to decline during New Deal Period and World War 2. By 1949, it had fallen to 22.5 percent. The corresponding share of 0.1 percent was down from 20 percent to 10 percent and for the 0.01 percent it fell from 10 percent to 4 percent. The period between 1950 and 1965 saw an increase in wealth inequality with the share of the top 1 percent going back to 25 percent. It fell to a new all-time low of 19 percent in 1970's and saw a significant bump in 1980's to 22 percent but it remained constant hereafter till 2000. The authors trace it to the creation of pension plans, mutual funds and financial innovation that led to a greater number of households participating in the stock market boom keeping the share of the top 1 percent in check. Indeed, today the share of the stock market in the wealth of the top 1 percent is at 38 percent which is lower than the general population.There was a great boom for Corporate America following the War but relatively high taxes (even excluding deductions, breaks, and loopholes) kept the return on corporate equity low.

Similarly, the Roosevelt administration hit the top wealth holders with estate taxes and even gift taxes which were not so easy to evade. There was an increase in income taxes as well but as I have pointed out in another answer, there was a relatively little impact in the period between 1932 and 1940, as the share of the top 10 percent remained at 40 percent before falling dramatically and remaining there till 1980's. The result might appear somewhat surprising given the general trend of rising inequality. But as Saez points out, it was income inequality that increased dramatically and not wealth inequality. This is not contradictory as it sounds. The share of labor income, as opposed to Capital, has declined but much of that can be traced to increase in the value of housing because of the Housing Bubble. As the economist Peter Ozark pointed out, it was labor income and not Capital income that increased inequality because of rising compensation for executives, people in the financial sector and to a lesser extent high tech sector. Piketty, Saez et al have estimated that it could take one or two decades for a top 0.1 percent income earner to enter into 0.1 percent of wealth earner even with good investments and high saving rate.

Year	Federal Reserve	EPI	Saez
1962	31.6	33.4	24.4
1983	31.5	33.8	21.1
1989	30.4	37.4	22.0
1992	30.2	NA	21.2
1995	34.6	NA	21.5
1998	33.9	38.1	21.7
2001	32.7	33.4	21.8
2004	33.4	34.3	NA
2007	33.8	34.6	NA

(This chart was prepared by Alan Reynolds of Cato Institute).

Reference:

Top Wealth Shares in the United States, 1916-2000: Evidence from Estate Tax Returns by Wojciech Kopczuk and Emmanuel Saez; Columbia University.